The probability of earning more than 10 percent on long-term corporate bonds. Introduction: The Normal distribution curve is a bell-shaped curve formed based on the frequency distribution of the observations The mean or average of the observations and their standard deviation define the normal distribution curve. Standard deviation refers to the variation in the actual observations from the average. Z-Score helps to know how many numbers of standard deviations is the raw score or outcome away from the average or mean.

Question

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Answer 1

Question

Chapter 10, Problem 28QP

a)

Summary Introduction

To determine: The probability of earning more than 10 percent on long-term corporate bonds.

Introduction:

The Normal distribution curve is a bell-shaped curve formed based on the frequency distribution of the observations The mean or average of the observations and their standard deviation define the normal distribution curve.

Standard deviation refers to the variation in the actual observations from the average.

Z-Score helps to know how many numbers of standard deviations is the raw score or outcome away from the average or mean.

a)

Expert Solution

Answer to Problem 28QP

The probability of earning more than 10 percent on long-term corporate bonds is 33.41 percent.

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return greater than 10 percent on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 1

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 2

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 3

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having more than 10 percent returns. Hence, “X” equals 10 percent. The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 4

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 5

The probability of 0.665882 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10 percent return. The area to the right of Z is the probability of getting a return of 10 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.665882. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10 percent return or more is 0.334118 or 33.4118 percent(1−0.665882).

Summary Introduction

To determine: The probability of earning less than 0 percent on long-term corporate bonds

Expert Solution

Answer to Problem 28QP

The probability of earning less than 0 percent on long-term corporate bonds is 0.223058 or 0.223058 percent

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return less than 0 percent on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 6

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 7

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 8

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (0 percent) return or less. Hence, “X” equals (0 percent). The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 9

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 10

The probability of 0.223058 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (0 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning less than 0 percent is 0.223058 or 0.223058 percent.

b)

Summary Introduction

To determine: The probability of earning more than 10 percent on Treasury bills

b)

Expert Solution

Answer to Problem 28QP

The probability of earning more than 10 percent on Treasury bills is 0.018006785 or 1.80 percent.

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the textbook).

Determine the probability of having a return greater than 10 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 11

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 12

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 13

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having more than 10 percent returns. Hence, “X” equals 10 percent. The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 14

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 15

The probability of 0.981993215 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10 percent return. The area to the right of Z is the probability of getting a return of 10 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.981993215. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10 percent return or more is 0.018006785 or 1.80 percent(1−0.981993215).

Summary Introduction

To determine: The probability of earning less than 0 percent on Treasury bills.

Expert Solution

Answer to Problem 28QP

The probability of earning less than 0 percent on Treasury bills is 0.129442113 or 12.94 percent.

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return less than 0 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 16

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 17

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 18

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (0 percent) return or less. Hence, “X” equals (0 percent). The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 19

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 20

The probability of 0.129442113 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (0 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning less than 0 percent is 0.129442113 or 12.94 percent.

c)

Summary Introduction

To determine: The probability of earning (4.18 percent) on long-term corporate bonds.

c)

Expert Solution

Answer to Problem 28QP

The probability of earning (4.18 percent) on long-term corporate bonds is 0.1039 or 10.39 percent.

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the textbook).

Determine the probability of having (4.18 percent) on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 21

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 22

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 23

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (4.18 percent) return or less. Hence, “X” equals (4.18 percent). The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 24

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 25

The probability of 0.103921 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (4.18 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning (4.18 percent) is 0.1039 or 10.39 percent.

Summary Introduction

To determine: The probability of earning 10.56 percent on Treasury bills.

Expert Solution

Answer to Problem 28QP

The probability of earning 10.56 percent on Treasury bills is 0.011380598 or 1.14 percent

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return of 10.56 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 26

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 27

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 28

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having 10.56 percent returns. Hence, “X” equals 10.56 percent. The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 29

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 30

The probability of 0.988619402 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10.56 percent return. The area to the right of Z is the probability of getting a return of 10.56 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.988619402. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10.56 percent return or more is 0.011380598 or 1.14 percent(1−0.988619402).

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Answer 2

Question

Chapter 10, Problem 28QP

a)

Summary Introduction

To determine: The probability of earning more than 10 percent on long-term corporate bonds.

Introduction:

The Normal distribution curve is a bell-shaped curve formed based on the frequency distribution of the observations The mean or average of the observations and their standard deviation define the normal distribution curve.

Standard deviation refers to the variation in the actual observations from the average.

Z-Score helps to know how many numbers of standard deviations is the raw score or outcome away from the average or mean.

a)

Expert Solution

Answer to Problem 28QP

The probability of earning more than 10 percent on long-term corporate bonds is 33.41 percent.

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return greater than 10 percent on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 1

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 2

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 3

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having more than 10 percent returns. Hence, “X” equals 10 percent. The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 4

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 5

The probability of 0.665882 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10 percent return. The area to the right of Z is the probability of getting a return of 10 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.665882. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10 percent return or more is 0.334118 or 33.4118 percent(1−0.665882).

Summary Introduction

To determine: The probability of earning less than 0 percent on long-term corporate bonds

Expert Solution

Answer to Problem 28QP

The probability of earning less than 0 percent on long-term corporate bonds is 0.223058 or 0.223058 percent

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return less than 0 percent on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 6

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 7

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 8

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (0 percent) return or less. Hence, “X” equals (0 percent). The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 9

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 10

The probability of 0.223058 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (0 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning less than 0 percent is 0.223058 or 0.223058 percent.

b)

Summary Introduction

To determine: The probability of earning more than 10 percent on Treasury bills

b)

Expert Solution

Answer to Problem 28QP

The probability of earning more than 10 percent on Treasury bills is 0.018006785 or 1.80 percent.

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the textbook).

Determine the probability of having a return greater than 10 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 11

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 12

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 13

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having more than 10 percent returns. Hence, “X” equals 10 percent. The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 14

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 15

The probability of 0.981993215 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10 percent return. The area to the right of Z is the probability of getting a return of 10 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.981993215. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10 percent return or more is 0.018006785 or 1.80 percent(1−0.981993215).

Summary Introduction

To determine: The probability of earning less than 0 percent on Treasury bills.

Expert Solution

Answer to Problem 28QP

The probability of earning less than 0 percent on Treasury bills is 0.129442113 or 12.94 percent.

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return less than 0 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 16

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 17

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 18

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (0 percent) return or less. Hence, “X” equals (0 percent). The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 19

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 20

The probability of 0.129442113 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (0 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning less than 0 percent is 0.129442113 or 12.94 percent.

c)

Summary Introduction

To determine: The probability of earning (4.18 percent) on long-term corporate bonds.

c)

Expert Solution

Answer to Problem 28QP

The probability of earning (4.18 percent) on long-term corporate bonds is 0.1039 or 10.39 percent.

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the textbook).

Determine the probability of having (4.18 percent) on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 21

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 22

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 23

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (4.18 percent) return or less. Hence, “X” equals (4.18 percent). The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 24

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 25

The probability of 0.103921 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (4.18 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning (4.18 percent) is 0.1039 or 10.39 percent.

Summary Introduction

To determine: The probability of earning 10.56 percent on Treasury bills.

Expert Solution

Answer to Problem 28QP

The probability of earning 10.56 percent on Treasury bills is 0.011380598 or 1.14 percent

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return of 10.56 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 26

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 27

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 28

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having 10.56 percent returns. Hence, “X” equals 10.56 percent. The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 29

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 30

The probability of 0.988619402 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10.56 percent return. The area to the right of Z is the probability of getting a return of 10.56 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.988619402. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10.56 percent return or more is 0.011380598 or 1.14 percent(1−0.988619402).

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Answer 3

Question

Chapter 10, Problem 28QP

a)

Summary Introduction

To determine: The probability of earning more than 10 percent on long-term corporate bonds.

Introduction:

The Normal distribution curve is a bell-shaped curve formed based on the frequency distribution of the observations The mean or average of the observations and their standard deviation define the normal distribution curve.

Standard deviation refers to the variation in the actual observations from the average.

Z-Score helps to know how many numbers of standard deviations is the raw score or outcome away from the average or mean.

a)

Expert Solution

Answer to Problem 28QP

The probability of earning more than 10 percent on long-term corporate bonds is 33.41 percent.

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return greater than 10 percent on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 1

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 2

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 3

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having more than 10 percent returns. Hence, “X” equals 10 percent. The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 4

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 5

The probability of 0.665882 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10 percent return. The area to the right of Z is the probability of getting a return of 10 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.665882. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10 percent return or more is 0.334118 or 33.4118 percent(1−0.665882).

Summary Introduction

To determine: The probability of earning less than 0 percent on long-term corporate bonds

Expert Solution

Answer to Problem 28QP

The probability of earning less than 0 percent on long-term corporate bonds is 0.223058 or 0.223058 percent

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return less than 0 percent on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 6

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 7

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 8

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (0 percent) return or less. Hence, “X” equals (0 percent). The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 9

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 10

The probability of 0.223058 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (0 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning less than 0 percent is 0.223058 or 0.223058 percent.

b)

Summary Introduction

To determine: The probability of earning more than 10 percent on Treasury bills

b)

Expert Solution

Answer to Problem 28QP

The probability of earning more than 10 percent on Treasury bills is 0.018006785 or 1.80 percent.

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the textbook).

Determine the probability of having a return greater than 10 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 11

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 12

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 13

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having more than 10 percent returns. Hence, “X” equals 10 percent. The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 14

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 15

The probability of 0.981993215 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10 percent return. The area to the right of Z is the probability of getting a return of 10 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.981993215. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10 percent return or more is 0.018006785 or 1.80 percent(1−0.981993215).

Summary Introduction

To determine: The probability of earning less than 0 percent on Treasury bills.

Expert Solution

Answer to Problem 28QP

The probability of earning less than 0 percent on Treasury bills is 0.129442113 or 12.94 percent.

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return less than 0 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 16

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 17

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 18

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (0 percent) return or less. Hence, “X” equals (0 percent). The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 19

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 20

The probability of 0.129442113 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (0 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning less than 0 percent is 0.129442113 or 12.94 percent.

c)

Summary Introduction

To determine: The probability of earning (4.18 percent) on long-term corporate bonds.

c)

Expert Solution

Answer to Problem 28QP

The probability of earning (4.18 percent) on long-term corporate bonds is 0.1039 or 10.39 percent.

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the textbook).

Determine the probability of having (4.18 percent) on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 21

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 22

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 23

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (4.18 percent) return or less. Hence, “X” equals (4.18 percent). The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 24

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 25

The probability of 0.103921 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (4.18 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning (4.18 percent) is 0.1039 or 10.39 percent.

Summary Introduction

To determine: The probability of earning 10.56 percent on Treasury bills.

Expert Solution

Answer to Problem 28QP

The probability of earning 10.56 percent on Treasury bills is 0.011380598 or 1.14 percent

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return of 10.56 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 26

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 27

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 28

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having 10.56 percent returns. Hence, “X” equals 10.56 percent. The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 29

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 30

The probability of 0.988619402 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10.56 percent return. The area to the right of Z is the probability of getting a return of 10.56 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.988619402. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10.56 percent return or more is 0.011380598 or 1.14 percent(1−0.988619402).

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 10, Problem 28QP

a)

Summary Introduction

To determine: The probability of earning more than 10 percent on long-term corporate bonds.

Introduction:

The Normal distribution curve is a bell-shaped curve formed based on the frequency distribution of the observations The mean or average of the observations and their standard deviation define the normal distribution curve.

Standard deviation refers to the variation in the actual observations from the average.

Z-Score helps to know how many numbers of standard deviations is the raw score or outcome away from the average or mean.

a)

Expert Solution

Answer to Problem 28QP

The probability of earning more than 10 percent on long-term corporate bonds is 33.41 percent.

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return greater than 10 percent on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 1

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 2

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 3

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having more than 10 percent returns. Hence, “X” equals 10 percent. The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 4

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 5

The probability of 0.665882 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10 percent return. The area to the right of Z is the probability of getting a return of 10 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.665882. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10 percent return or more is 0.334118 or 33.4118 percent(1−0.665882).

Summary Introduction

To determine: The probability of earning less than 0 percent on long-term corporate bonds

Expert Solution

Answer to Problem 28QP

The probability of earning less than 0 percent on long-term corporate bonds is 0.223058 or 0.223058 percent

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return less than 0 percent on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 6

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 7

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 8

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (0 percent) return or less. Hence, “X” equals (0 percent). The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 9

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 10

The probability of 0.223058 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (0 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning less than 0 percent is 0.223058 or 0.223058 percent.

b)

Summary Introduction

To determine: The probability of earning more than 10 percent on Treasury bills

b)

Expert Solution

Answer to Problem 28QP

The probability of earning more than 10 percent on Treasury bills is 0.018006785 or 1.80 percent.

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the textbook).

Determine the probability of having a return greater than 10 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 11

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 12

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 13

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having more than 10 percent returns. Hence, “X” equals 10 percent. The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 14

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 15

The probability of 0.981993215 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10 percent return. The area to the right of Z is the probability of getting a return of 10 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.981993215. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10 percent return or more is 0.018006785 or 1.80 percent(1−0.981993215).

Summary Introduction

To determine: The probability of earning less than 0 percent on Treasury bills.

Expert Solution

Answer to Problem 28QP

The probability of earning less than 0 percent on Treasury bills is 0.129442113 or 12.94 percent.

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return less than 0 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 16

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 17

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 18

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (0 percent) return or less. Hence, “X” equals (0 percent). The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 19

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 20

The probability of 0.129442113 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (0 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning less than 0 percent is 0.129442113 or 12.94 percent.

c)

Summary Introduction

To determine: The probability of earning (4.18 percent) on long-term corporate bonds.

c)

Expert Solution

Answer to Problem 28QP

The probability of earning (4.18 percent) on long-term corporate bonds is 0.1039 or 10.39 percent.

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the textbook).

Determine the probability of having (4.18 percent) on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 21

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 22

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 23

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (4.18 percent) return or less. Hence, “X” equals (4.18 percent). The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 24

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 25

The probability of 0.103921 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (4.18 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning (4.18 percent) is 0.1039 or 10.39 percent.

Summary Introduction

To determine: The probability of earning 10.56 percent on Treasury bills.

Expert Solution

Answer to Problem 28QP

The probability of earning 10.56 percent on Treasury bills is 0.011380598 or 1.14 percent

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return of 10.56 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 26

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 27

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 28

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having 10.56 percent returns. Hence, “X” equals 10.56 percent. The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 29

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 30

The probability of 0.988619402 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10.56 percent return. The area to the right of Z is the probability of getting a return of 10.56 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.988619402. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10.56 percent return or more is 0.011380598 or 1.14 percent(1−0.988619402).

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 10, Problem 28QP

a)

Summary Introduction

To determine: The probability of earning more than 10 percent on long-term corporate bonds.

Introduction:

The Normal distribution curve is a bell-shaped curve formed based on the frequency distribution of the observations The mean or average of the observations and their standard deviation define the normal distribution curve.

Standard deviation refers to the variation in the actual observations from the average.

Z-Score helps to know how many numbers of standard deviations is the raw score or outcome away from the average or mean.

a)

Expert Solution

Answer to Problem 28QP

The probability of earning more than 10 percent on long-term corporate bonds is 33.41 percent.

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return greater than 10 percent on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 1

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 2

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 3

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having more than 10 percent returns. Hence, “X” equals 10 percent. The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 4

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 5

The probability of 0.665882 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10 percent return. The area to the right of Z is the probability of getting a return of 10 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.665882. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10 percent return or more is 0.334118 or 33.4118 percent(1−0.665882).

Summary Introduction

To determine: The probability of earning less than 0 percent on long-term corporate bonds

Expert Solution

Answer to Problem 28QP

The probability of earning less than 0 percent on long-term corporate bonds is 0.223058 or 0.223058 percent

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return less than 0 percent on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 6

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 7

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 8

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (0 percent) return or less. Hence, “X” equals (0 percent). The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 9

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 10

The probability of 0.223058 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (0 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning less than 0 percent is 0.223058 or 0.223058 percent.

b)

Summary Introduction

To determine: The probability of earning more than 10 percent on Treasury bills

b)

Expert Solution

Answer to Problem 28QP

The probability of earning more than 10 percent on Treasury bills is 0.018006785 or 1.80 percent.

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the textbook).

Determine the probability of having a return greater than 10 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 11

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 12

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 13

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having more than 10 percent returns. Hence, “X” equals 10 percent. The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 14

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 15

The probability of 0.981993215 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10 percent return. The area to the right of Z is the probability of getting a return of 10 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.981993215. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10 percent return or more is 0.018006785 or 1.80 percent(1−0.981993215).

Summary Introduction

To determine: The probability of earning less than 0 percent on Treasury bills.

Expert Solution

Answer to Problem 28QP

The probability of earning less than 0 percent on Treasury bills is 0.129442113 or 12.94 percent.

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return less than 0 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 16

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 17

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 18

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (0 percent) return or less. Hence, “X” equals (0 percent). The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 19

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 20

The probability of 0.129442113 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (0 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning less than 0 percent is 0.129442113 or 12.94 percent.

c)

Summary Introduction

To determine: The probability of earning (4.18 percent) on long-term corporate bonds.

c)

Expert Solution

Answer to Problem 28QP

The probability of earning (4.18 percent) on long-term corporate bonds is 0.1039 or 10.39 percent.

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the textbook).

Determine the probability of having (4.18 percent) on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 21

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 22

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 23

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (4.18 percent) return or less. Hence, “X” equals (4.18 percent). The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 24

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 25

The probability of 0.103921 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (4.18 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning (4.18 percent) is 0.1039 or 10.39 percent.

Summary Introduction

To determine: The probability of earning 10.56 percent on Treasury bills.

Expert Solution

Answer to Problem 28QP

The probability of earning 10.56 percent on Treasury bills is 0.011380598 or 1.14 percent

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return of 10.56 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 26

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 27

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 28

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having 10.56 percent returns. Hence, “X” equals 10.56 percent. The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 29

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 30

The probability of 0.988619402 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10.56 percent return. The area to the right of Z is the probability of getting a return of 10.56 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.988619402. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10.56 percent return or more is 0.011380598 or 1.14 percent(1−0.988619402).

Answer 6

Chapter 10, Problem 28QP

a)

Summary Introduction

To determine: The probability of earning more than 10 percent on long-term corporate bonds.

Introduction:

The Normal distribution curve is a bell-shaped curve formed based on the frequency distribution of the observations The mean or average of the observations and their standard deviation define the normal distribution curve.

Standard deviation refers to the variation in the actual observations from the average.

Z-Score helps to know how many numbers of standard deviations is the raw score or outcome away from the average or mean.

a)

Expert Solution

Answer to Problem 28QP

The probability of earning more than 10 percent on long-term corporate bonds is 33.41 percent.

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return greater than 10 percent on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 1

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 2

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 3

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having more than 10 percent returns. Hence, “X” equals 10 percent. The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 4

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 5

The probability of 0.665882 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10 percent return. The area to the right of Z is the probability of getting a return of 10 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.665882. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10 percent return or more is 0.334118 or 33.4118 percent(1−0.665882).

Answer 7

Chapter 10, Problem 28QP

a)

Summary Introduction

To determine: The probability of earning more than 10 percent on long-term corporate bonds.

Introduction:

The Normal distribution curve is a bell-shaped curve formed based on the frequency distribution of the observations The mean or average of the observations and their standard deviation define the normal distribution curve.

Standard deviation refers to the variation in the actual observations from the average.

Z-Score helps to know how many numbers of standard deviations is the raw score or outcome away from the average or mean.

Answer 8

a)

Expert Solution

Answer to Problem 28QP

The probability of earning more than 10 percent on long-term corporate bonds is 33.41 percent.

Answer 9

a)

Expert Solution

Answer 10

a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return greater than 10 percent on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 1

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 2

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 3

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having more than 10 percent returns. Hence, “X” equals 10 percent. The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 4

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 5

The probability of 0.665882 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10 percent return. The area to the right of Z is the probability of getting a return of 10 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.665882. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10 percent return or more is 0.334118 or 33.4118 percent(1−0.665882).

Answer 13

Summary Introduction

To determine: The probability of earning less than 0 percent on long-term corporate bonds

Expert Solution

Answer to Problem 28QP

The probability of earning less than 0 percent on long-term corporate bonds is 0.223058 or 0.223058 percent

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return less than 0 percent on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 6

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 7

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 8

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (0 percent) return or less. Hence, “X” equals (0 percent). The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 9

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 10

The probability of 0.223058 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (0 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning less than 0 percent is 0.223058 or 0.223058 percent.

Answer 14

Summary Introduction

To determine: The probability of earning less than 0 percent on long-term corporate bonds

Answer 15

Expert Solution

Answer to Problem 28QP

The probability of earning less than 0 percent on long-term corporate bonds is 0.223058 or 0.223058 percent

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return less than 0 percent on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 6

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 7

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 8

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (0 percent) return or less. Hence, “X” equals (0 percent). The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 9

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 10

The probability of 0.223058 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (0 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning less than 0 percent is 0.223058 or 0.223058 percent.

Answer 20

b)

Summary Introduction

To determine: The probability of earning more than 10 percent on Treasury bills

b)

Expert Solution

Answer to Problem 28QP

The probability of earning more than 10 percent on Treasury bills is 0.018006785 or 1.80 percent.

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the textbook).

Determine the probability of having a return greater than 10 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 11

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 12

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 13

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having more than 10 percent returns. Hence, “X” equals 10 percent. The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 14

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 15

The probability of 0.981993215 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10 percent return. The area to the right of Z is the probability of getting a return of 10 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.981993215. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10 percent return or more is 0.018006785 or 1.80 percent(1−0.981993215).

Answer 21

b)

Summary Introduction

To determine: The probability of earning more than 10 percent on Treasury bills

Answer 22

b)

Expert Solution

Answer to Problem 28QP

The probability of earning more than 10 percent on Treasury bills is 0.018006785 or 1.80 percent.

Answer 23

b)

Expert Solution

Answer 24

b)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the textbook).

Determine the probability of having a return greater than 10 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 11

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 12

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 13

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having more than 10 percent returns. Hence, “X” equals 10 percent. The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 14

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 15

The probability of 0.981993215 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10 percent return. The area to the right of Z is the probability of getting a return of 10 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.981993215. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10 percent return or more is 0.018006785 or 1.80 percent(1−0.981993215).

Answer 27

Summary Introduction

To determine: The probability of earning less than 0 percent on Treasury bills.

Expert Solution

Answer to Problem 28QP

The probability of earning less than 0 percent on Treasury bills is 0.129442113 or 12.94 percent.

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return less than 0 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 16

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 17

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 18

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (0 percent) return or less. Hence, “X” equals (0 percent). The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 19

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 20

The probability of 0.129442113 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (0 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning less than 0 percent is 0.129442113 or 12.94 percent.

Answer 28

Summary Introduction

To determine: The probability of earning less than 0 percent on Treasury bills.

Answer 29

Expert Solution

Answer to Problem 28QP

The probability of earning less than 0 percent on Treasury bills is 0.129442113 or 12.94 percent.

Answer 30

Expert Solution

Answer 31

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return less than 0 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 16

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 17

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 18

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (0 percent) return or less. Hence, “X” equals (0 percent). The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 19

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 20

The probability of 0.129442113 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (0 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning less than 0 percent is 0.129442113 or 12.94 percent.

Answer 34

c)

Summary Introduction

To determine: The probability of earning (4.18 percent) on long-term corporate bonds.

c)

Expert Solution

Answer to Problem 28QP

The probability of earning (4.18 percent) on long-term corporate bonds is 0.1039 or 10.39 percent.

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the textbook).

Determine the probability of having (4.18 percent) on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 21

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 22

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 23

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (4.18 percent) return or less. Hence, “X” equals (4.18 percent). The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 24

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 25

The probability of 0.103921 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (4.18 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning (4.18 percent) is 0.1039 or 10.39 percent.

Answer 35

c)

Summary Introduction

To determine: The probability of earning (4.18 percent) on long-term corporate bonds.

Answer 36

c)

Expert Solution

Answer to Problem 28QP

The probability of earning (4.18 percent) on long-term corporate bonds is 0.1039 or 10.39 percent.

Answer 37

c)

Expert Solution

Answer 38

c)

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the textbook).

Determine the probability of having (4.18 percent) on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 21

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 22

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 23

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (4.18 percent) return or less. Hence, “X” equals (4.18 percent). The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 24

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 25

The probability of 0.103921 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (4.18 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning (4.18 percent) is 0.1039 or 10.39 percent.

Answer 41

Summary Introduction

To determine: The probability of earning 10.56 percent on Treasury bills.

Expert Solution

Answer to Problem 28QP

The probability of earning 10.56 percent on Treasury bills is 0.011380598 or 1.14 percent

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return of 10.56 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 26

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 27

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 28

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having 10.56 percent returns. Hence, “X” equals 10.56 percent. The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 29

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 30

The probability of 0.988619402 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10.56 percent return. The area to the right of Z is the probability of getting a return of 10.56 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.988619402. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10.56 percent return or more is 0.011380598 or 1.14 percent(1−0.988619402).

Answer 42

Summary Introduction

To determine: The probability of earning 10.56 percent on Treasury bills.

Answer 43

Expert Solution

Answer to Problem 28QP

The probability of earning 10.56 percent on Treasury bills is 0.011380598 or 1.14 percent

Answer 44

Expert Solution

Answer 45

Expert Solution

Answer 46

Expert Solution

Answer 47

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return of 10.56 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 26

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 27

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 28

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having 10.56 percent returns. Hence, “X” equals 10.56 percent. The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 29

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance, Chapter 10, Problem 28QP , additional homework tip 30

The probability of 0.988619402 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10.56 percent return. The area to the right of Z is the probability of getting a return of 10.56 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.988619402. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10.56 percent return or more is 0.011380598 or 1.14 percent(1−0.988619402).