Find the area under the standard normal distribution for each. a . Between 0 and 1.50 b . Between 0 and −1.25 c . Between 1.56 and 1.96 d . Between −1.20 and −2.25 e . Between −0.06 and 0.73 f . Between 1.10 and −1.80 g . To the right of z = 1.75 h . To the right of z = −1.28 i . To the left of z = −2.12 j . To the left of z = 1.36

Question

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Answer 1

Textbook Question

Chapter 6, Problem 18CQ

Find the area under the standard normal distribution for each.

a. Between 0 and 1.50

b. Between 0 and −1.25

c. Between 1.56 and 1.96

d. Between −1.20 and −2.25

e. Between −0.06 and 0.73

f. Between 1.10 and −1.80

g. To the right of z = 1.75

h. To the right of z = −1.28

i. To the left of z = −2.12

j. To the left of z = 1.36

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

(a)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 0 and 1.50. That is, P(0<z<1.50).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 0 and 1.50 is 0.433.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 0 and 1.50 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value 0 for X value1 and then the larger value 1.50 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 1

Therefore, P(0<z<1.50)=0.433.

Conclusion:

The area under the standard normal distribution curve for z lies between 0 and 1.50 is 0.433.

(b)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 0 and

–1.25. That is, P(−1.25<z<0).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 0 and -1.25 is 0.394.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 0 and -1.25 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -1.25 for X value1 and then the larger value 0 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 2

Therefore, P(−1.25<z<0)=0.394.

Conclusion:

The area under the standard normal distribution curve for z lies between 0 and -1.25 is 0.394.

(c)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 1.56 and 1.96. That is, P(1.56<z<1.96).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 1.56 and 1.96 is 0.0344.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 1.56 and 1.96 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value 1.56 for X value1 and then the larger value 1.96 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 3 .

Therefore, P(1.56<z<1.96)=0.0344.

Conclusion:

The area under the standard normal distribution curve for z lies between 1.56 and 1.96 is 0.0344.

(d)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between -1.20 and –2.25. That is, P(−2.25<z<−1.20).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between -1.20 and -2.25 is 0.103.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between -1.20 and -2.25 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -2.25 for X value1 and then the larger value -1.20 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 4

Therefore, P(−2.25<z<−1.20)=0.103 .

Conclusion:

The area under the standard normal distribution curve for z lies between -1.20 and -2.25 is 0.103.

(e)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between -0.06 and 0.73. That is, P(−0.06<z<0.73).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between -0.06 and 0.73 is 0.291.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between -0.06 and 0.73 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -0.06 for X value1 and then the larger value 0.73 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 5 .

Therefore, P(−0.06<z<0.73)=0.291

Conclusion:

The area under the standard normal distribution curve for z lies between -0.06 and 0.73 is 0.291.

(f)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 1.10 and -1.80. That is, P(−1.80<z<1.10).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 1.10 and -1.80 is 0.828.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 1.10 and -1.80 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -1.80 for X value1 and then the larger value 1.10 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 6

Therefore, P(−1.80<z<1.10)=0.828.

Conclusion:

The area under the standard normal distribution curve for z lies between 1.10 and -1.80 is 0.828.

(g)

Expert Solution

To determine

To find: The area under the standard normal curve to the right of z=1.75.

Answer to Problem 18CQ

The area under the standard normal curve to the right of z=1.75 is 0.0401.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the right of 1.75 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Right Trail.
Type in the Z value of 1.75 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 7

Therefore, P(z>1.75)=0.0401.

Conclusion:

The area under the standard normal curve to the right of z=1.75 is 0.0401.

(h)

Expert Solution

To determine

To find: The area under the standard normal curve to the right of z=−1.28.

Answer to Problem 18CQ

The area under the standard normal curve to the right of z=−1.28 is 0.8997.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the right of -1.28 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Right Trail.
Type in the Z value of -1.28 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 8

Therefore, P(z>−1.28)=0.8997

Conclusion:

The area under the standard normal curve to the right of z=−1.28 is 0.8997.

(i)

Expert Solution

To determine

To find: The area under the standard normal curve to the left of z=−2.12.

Answer to Problem 18CQ

The area under the standard normal curve to the left of z=−2.12 is 0.0170.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the left of -2.12 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Left Trail.
Type in the Z value of -2.12 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 9

Therefore, P(z<−2.12)=0.0170.

Conclusion:

The area under the standard normal curve to the left of z=−2.12 is 0.0170.

(j)

Expert Solution

To determine

To find: The area under the standard normal curve to the left of z=1.36.

Answer to Problem 18CQ

The area under the standard normal curve to the left of z=1.36 is 0.913.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the left of 1.36 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Left Trail.
Type in the Z value of 1.36 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 10

Therefore, P(z<1.36)=0.913.

Conclusion:

The area under the standard normal curve to the left of z=1.36 is 0.913.

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Answer 2

Textbook Question

Chapter 6, Problem 18CQ

Find the area under the standard normal distribution for each.

a. Between 0 and 1.50

b. Between 0 and −1.25

c. Between 1.56 and 1.96

d. Between −1.20 and −2.25

e. Between −0.06 and 0.73

f. Between 1.10 and −1.80

g. To the right of z = 1.75

h. To the right of z = −1.28

i. To the left of z = −2.12

j. To the left of z = 1.36

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

(a)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 0 and 1.50. That is, P(0<z<1.50).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 0 and 1.50 is 0.433.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 0 and 1.50 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value 0 for X value1 and then the larger value 1.50 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 1

Therefore, P(0<z<1.50)=0.433.

Conclusion:

The area under the standard normal distribution curve for z lies between 0 and 1.50 is 0.433.

(b)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 0 and

–1.25. That is, P(−1.25<z<0).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 0 and -1.25 is 0.394.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 0 and -1.25 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -1.25 for X value1 and then the larger value 0 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 2

Therefore, P(−1.25<z<0)=0.394.

Conclusion:

The area under the standard normal distribution curve for z lies between 0 and -1.25 is 0.394.

(c)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 1.56 and 1.96. That is, P(1.56<z<1.96).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 1.56 and 1.96 is 0.0344.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 1.56 and 1.96 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value 1.56 for X value1 and then the larger value 1.96 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 3 .

Therefore, P(1.56<z<1.96)=0.0344.

Conclusion:

The area under the standard normal distribution curve for z lies between 1.56 and 1.96 is 0.0344.

(d)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between -1.20 and –2.25. That is, P(−2.25<z<−1.20).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between -1.20 and -2.25 is 0.103.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between -1.20 and -2.25 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -2.25 for X value1 and then the larger value -1.20 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 4

Therefore, P(−2.25<z<−1.20)=0.103 .

Conclusion:

The area under the standard normal distribution curve for z lies between -1.20 and -2.25 is 0.103.

(e)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between -0.06 and 0.73. That is, P(−0.06<z<0.73).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between -0.06 and 0.73 is 0.291.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between -0.06 and 0.73 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -0.06 for X value1 and then the larger value 0.73 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 5 .

Therefore, P(−0.06<z<0.73)=0.291

Conclusion:

The area under the standard normal distribution curve for z lies between -0.06 and 0.73 is 0.291.

(f)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 1.10 and -1.80. That is, P(−1.80<z<1.10).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 1.10 and -1.80 is 0.828.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 1.10 and -1.80 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -1.80 for X value1 and then the larger value 1.10 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 6

Therefore, P(−1.80<z<1.10)=0.828.

Conclusion:

The area under the standard normal distribution curve for z lies between 1.10 and -1.80 is 0.828.

(g)

Expert Solution

To determine

To find: The area under the standard normal curve to the right of z=1.75.

Answer to Problem 18CQ

The area under the standard normal curve to the right of z=1.75 is 0.0401.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the right of 1.75 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Right Trail.
Type in the Z value of 1.75 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 7

Therefore, P(z>1.75)=0.0401.

Conclusion:

The area under the standard normal curve to the right of z=1.75 is 0.0401.

(h)

Expert Solution

To determine

To find: The area under the standard normal curve to the right of z=−1.28.

Answer to Problem 18CQ

The area under the standard normal curve to the right of z=−1.28 is 0.8997.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the right of -1.28 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Right Trail.
Type in the Z value of -1.28 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 8

Therefore, P(z>−1.28)=0.8997

Conclusion:

The area under the standard normal curve to the right of z=−1.28 is 0.8997.

(i)

Expert Solution

To determine

To find: The area under the standard normal curve to the left of z=−2.12.

Answer to Problem 18CQ

The area under the standard normal curve to the left of z=−2.12 is 0.0170.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the left of -2.12 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Left Trail.
Type in the Z value of -2.12 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 9

Therefore, P(z<−2.12)=0.0170.

Conclusion:

The area under the standard normal curve to the left of z=−2.12 is 0.0170.

(j)

Expert Solution

To determine

To find: The area under the standard normal curve to the left of z=1.36.

Answer to Problem 18CQ

The area under the standard normal curve to the left of z=1.36 is 0.913.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the left of 1.36 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Left Trail.
Type in the Z value of 1.36 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 10

Therefore, P(z<1.36)=0.913.

Conclusion:

The area under the standard normal curve to the left of z=1.36 is 0.913.

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Answer 3

Textbook Question

Chapter 6, Problem 18CQ

Find the area under the standard normal distribution for each.

a. Between 0 and 1.50

b. Between 0 and −1.25

c. Between 1.56 and 1.96

d. Between −1.20 and −2.25

e. Between −0.06 and 0.73

f. Between 1.10 and −1.80

g. To the right of z = 1.75

h. To the right of z = −1.28

i. To the left of z = −2.12

j. To the left of z = 1.36

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

(a)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 0 and 1.50. That is, P(0<z<1.50).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 0 and 1.50 is 0.433.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 0 and 1.50 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value 0 for X value1 and then the larger value 1.50 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 1

Therefore, P(0<z<1.50)=0.433.

Conclusion:

The area under the standard normal distribution curve for z lies between 0 and 1.50 is 0.433.

(b)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 0 and

–1.25. That is, P(−1.25<z<0).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 0 and -1.25 is 0.394.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 0 and -1.25 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -1.25 for X value1 and then the larger value 0 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 2

Therefore, P(−1.25<z<0)=0.394.

Conclusion:

The area under the standard normal distribution curve for z lies between 0 and -1.25 is 0.394.

(c)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 1.56 and 1.96. That is, P(1.56<z<1.96).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 1.56 and 1.96 is 0.0344.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 1.56 and 1.96 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value 1.56 for X value1 and then the larger value 1.96 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 3 .

Therefore, P(1.56<z<1.96)=0.0344.

Conclusion:

The area under the standard normal distribution curve for z lies between 1.56 and 1.96 is 0.0344.

(d)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between -1.20 and –2.25. That is, P(−2.25<z<−1.20).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between -1.20 and -2.25 is 0.103.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between -1.20 and -2.25 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -2.25 for X value1 and then the larger value -1.20 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 4

Therefore, P(−2.25<z<−1.20)=0.103 .

Conclusion:

The area under the standard normal distribution curve for z lies between -1.20 and -2.25 is 0.103.

(e)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between -0.06 and 0.73. That is, P(−0.06<z<0.73).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between -0.06 and 0.73 is 0.291.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between -0.06 and 0.73 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -0.06 for X value1 and then the larger value 0.73 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 5 .

Therefore, P(−0.06<z<0.73)=0.291

Conclusion:

The area under the standard normal distribution curve for z lies between -0.06 and 0.73 is 0.291.

(f)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 1.10 and -1.80. That is, P(−1.80<z<1.10).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 1.10 and -1.80 is 0.828.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 1.10 and -1.80 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -1.80 for X value1 and then the larger value 1.10 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 6

Therefore, P(−1.80<z<1.10)=0.828.

Conclusion:

The area under the standard normal distribution curve for z lies between 1.10 and -1.80 is 0.828.

(g)

Expert Solution

To determine

To find: The area under the standard normal curve to the right of z=1.75.

Answer to Problem 18CQ

The area under the standard normal curve to the right of z=1.75 is 0.0401.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the right of 1.75 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Right Trail.
Type in the Z value of 1.75 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 7

Therefore, P(z>1.75)=0.0401.

Conclusion:

The area under the standard normal curve to the right of z=1.75 is 0.0401.

(h)

Expert Solution

To determine

To find: The area under the standard normal curve to the right of z=−1.28.

Answer to Problem 18CQ

The area under the standard normal curve to the right of z=−1.28 is 0.8997.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the right of -1.28 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Right Trail.
Type in the Z value of -1.28 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 8

Therefore, P(z>−1.28)=0.8997

Conclusion:

The area under the standard normal curve to the right of z=−1.28 is 0.8997.

(i)

Expert Solution

To determine

To find: The area under the standard normal curve to the left of z=−2.12.

Answer to Problem 18CQ

The area under the standard normal curve to the left of z=−2.12 is 0.0170.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the left of -2.12 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Left Trail.
Type in the Z value of -2.12 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 9

Therefore, P(z<−2.12)=0.0170.

Conclusion:

The area under the standard normal curve to the left of z=−2.12 is 0.0170.

(j)

Expert Solution

To determine

To find: The area under the standard normal curve to the left of z=1.36.

Answer to Problem 18CQ

The area under the standard normal curve to the left of z=1.36 is 0.913.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the left of 1.36 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Left Trail.
Type in the Z value of 1.36 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 10

Therefore, P(z<1.36)=0.913.

Conclusion:

The area under the standard normal curve to the left of z=1.36 is 0.913.

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Answer 4

Textbook Question

Chapter 6, Problem 18CQ

Find the area under the standard normal distribution for each.

a. Between 0 and 1.50

b. Between 0 and −1.25

c. Between 1.56 and 1.96

d. Between −1.20 and −2.25

e. Between −0.06 and 0.73

f. Between 1.10 and −1.80

g. To the right of z = 1.75

h. To the right of z = −1.28

i. To the left of z = −2.12

j. To the left of z = 1.36

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

(a)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 0 and 1.50. That is, P(0<z<1.50).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 0 and 1.50 is 0.433.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 0 and 1.50 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value 0 for X value1 and then the larger value 1.50 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 1

Therefore, P(0<z<1.50)=0.433.

Conclusion:

The area under the standard normal distribution curve for z lies between 0 and 1.50 is 0.433.

(b)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 0 and

–1.25. That is, P(−1.25<z<0).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 0 and -1.25 is 0.394.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 0 and -1.25 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -1.25 for X value1 and then the larger value 0 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 2

Therefore, P(−1.25<z<0)=0.394.

Conclusion:

The area under the standard normal distribution curve for z lies between 0 and -1.25 is 0.394.

(c)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 1.56 and 1.96. That is, P(1.56<z<1.96).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 1.56 and 1.96 is 0.0344.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 1.56 and 1.96 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value 1.56 for X value1 and then the larger value 1.96 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 3 .

Therefore, P(1.56<z<1.96)=0.0344.

Conclusion:

The area under the standard normal distribution curve for z lies between 1.56 and 1.96 is 0.0344.

(d)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between -1.20 and –2.25. That is, P(−2.25<z<−1.20).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between -1.20 and -2.25 is 0.103.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between -1.20 and -2.25 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -2.25 for X value1 and then the larger value -1.20 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 4

Therefore, P(−2.25<z<−1.20)=0.103 .

Conclusion:

The area under the standard normal distribution curve for z lies between -1.20 and -2.25 is 0.103.

(e)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between -0.06 and 0.73. That is, P(−0.06<z<0.73).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between -0.06 and 0.73 is 0.291.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between -0.06 and 0.73 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -0.06 for X value1 and then the larger value 0.73 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 5 .

Therefore, P(−0.06<z<0.73)=0.291

Conclusion:

The area under the standard normal distribution curve for z lies between -0.06 and 0.73 is 0.291.

(f)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 1.10 and -1.80. That is, P(−1.80<z<1.10).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 1.10 and -1.80 is 0.828.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 1.10 and -1.80 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -1.80 for X value1 and then the larger value 1.10 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 6

Therefore, P(−1.80<z<1.10)=0.828.

Conclusion:

The area under the standard normal distribution curve for z lies between 1.10 and -1.80 is 0.828.

(g)

Expert Solution

To determine

To find: The area under the standard normal curve to the right of z=1.75.

Answer to Problem 18CQ

The area under the standard normal curve to the right of z=1.75 is 0.0401.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the right of 1.75 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Right Trail.
Type in the Z value of 1.75 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 7

Therefore, P(z>1.75)=0.0401.

Conclusion:

The area under the standard normal curve to the right of z=1.75 is 0.0401.

(h)

Expert Solution

To determine

To find: The area under the standard normal curve to the right of z=−1.28.

Answer to Problem 18CQ

The area under the standard normal curve to the right of z=−1.28 is 0.8997.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the right of -1.28 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Right Trail.
Type in the Z value of -1.28 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 8

Therefore, P(z>−1.28)=0.8997

Conclusion:

The area under the standard normal curve to the right of z=−1.28 is 0.8997.

(i)

Expert Solution

To determine

To find: The area under the standard normal curve to the left of z=−2.12.

Answer to Problem 18CQ

The area under the standard normal curve to the left of z=−2.12 is 0.0170.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the left of -2.12 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Left Trail.
Type in the Z value of -2.12 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 9

Therefore, P(z<−2.12)=0.0170.

Conclusion:

The area under the standard normal curve to the left of z=−2.12 is 0.0170.

(j)

Expert Solution

To determine

To find: The area under the standard normal curve to the left of z=1.36.

Answer to Problem 18CQ

The area under the standard normal curve to the left of z=1.36 is 0.913.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the left of 1.36 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Left Trail.
Type in the Z value of 1.36 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 10

Therefore, P(z<1.36)=0.913.

Conclusion:

The area under the standard normal curve to the left of z=1.36 is 0.913.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

(a)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 0 and 1.50. That is, P(0<z<1.50).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 0 and 1.50 is 0.433.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 0 and 1.50 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value 0 for X value1 and then the larger value 1.50 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 1

Therefore, P(0<z<1.50)=0.433.

Conclusion:

The area under the standard normal distribution curve for z lies between 0 and 1.50 is 0.433.

(b)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 0 and

–1.25. That is, P(−1.25<z<0).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 0 and -1.25 is 0.394.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 0 and -1.25 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -1.25 for X value1 and then the larger value 0 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 2

Therefore, P(−1.25<z<0)=0.394.

Conclusion:

The area under the standard normal distribution curve for z lies between 0 and -1.25 is 0.394.

(c)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 1.56 and 1.96. That is, P(1.56<z<1.96).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 1.56 and 1.96 is 0.0344.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 1.56 and 1.96 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value 1.56 for X value1 and then the larger value 1.96 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 3 .

Therefore, P(1.56<z<1.96)=0.0344.

Conclusion:

The area under the standard normal distribution curve for z lies between 1.56 and 1.96 is 0.0344.

(d)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between -1.20 and –2.25. That is, P(−2.25<z<−1.20).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between -1.20 and -2.25 is 0.103.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between -1.20 and -2.25 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -2.25 for X value1 and then the larger value -1.20 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 4

Therefore, P(−2.25<z<−1.20)=0.103 .

Conclusion:

The area under the standard normal distribution curve for z lies between -1.20 and -2.25 is 0.103.

(e)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between -0.06 and 0.73. That is, P(−0.06<z<0.73).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between -0.06 and 0.73 is 0.291.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between -0.06 and 0.73 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -0.06 for X value1 and then the larger value 0.73 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 5 .

Therefore, P(−0.06<z<0.73)=0.291

Conclusion:

The area under the standard normal distribution curve for z lies between -0.06 and 0.73 is 0.291.

(f)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 1.10 and -1.80. That is, P(−1.80<z<1.10).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 1.10 and -1.80 is 0.828.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 1.10 and -1.80 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -1.80 for X value1 and then the larger value 1.10 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 6

Therefore, P(−1.80<z<1.10)=0.828.

Conclusion:

The area under the standard normal distribution curve for z lies between 1.10 and -1.80 is 0.828.

(g)

Expert Solution

To determine

To find: The area under the standard normal curve to the right of z=1.75.

Answer to Problem 18CQ

The area under the standard normal curve to the right of z=1.75 is 0.0401.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the right of 1.75 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Right Trail.
Type in the Z value of 1.75 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 7

Therefore, P(z>1.75)=0.0401.

Conclusion:

The area under the standard normal curve to the right of z=1.75 is 0.0401.

(h)

Expert Solution

To determine

To find: The area under the standard normal curve to the right of z=−1.28.

Answer to Problem 18CQ

The area under the standard normal curve to the right of z=−1.28 is 0.8997.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the right of -1.28 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Right Trail.
Type in the Z value of -1.28 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 8

Therefore, P(z>−1.28)=0.8997

Conclusion:

The area under the standard normal curve to the right of z=−1.28 is 0.8997.

(i)

Expert Solution

To determine

To find: The area under the standard normal curve to the left of z=−2.12.

Answer to Problem 18CQ

The area under the standard normal curve to the left of z=−2.12 is 0.0170.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the left of -2.12 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Left Trail.
Type in the Z value of -2.12 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 9

Therefore, P(z<−2.12)=0.0170.

Conclusion:

The area under the standard normal curve to the left of z=−2.12 is 0.0170.

(j)

Expert Solution

To determine

To find: The area under the standard normal curve to the left of z=1.36.

Answer to Problem 18CQ

The area under the standard normal curve to the left of z=1.36 is 0.913.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the left of 1.36 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Left Trail.
Type in the Z value of 1.36 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 10

Therefore, P(z<1.36)=0.913.

Conclusion:

The area under the standard normal curve to the left of z=1.36 is 0.913.

Answer 8

(a)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 0 and 1.50. That is, P(0<z<1.50).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 0 and 1.50 is 0.433.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 0 and 1.50 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value 0 for X value1 and then the larger value 1.50 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 1

Therefore, P(0<z<1.50)=0.433.

Conclusion:

The area under the standard normal distribution curve for z lies between 0 and 1.50 is 0.433.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

To find: The area under the standard normal distribution curve for z lies between 0 and 1.50. That is, P(0<z<1.50).

Answer 13

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 0 and 1.50 is 0.433.

Answer 14

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 0 and 1.50 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value 0 for X value1 and then the larger value 1.50 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 1

Therefore, P(0<z<1.50)=0.433.

Conclusion:

The area under the standard normal distribution curve for z lies between 0 and 1.50 is 0.433.

Answer 15

(b)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 0 and

–1.25. That is, P(−1.25<z<0).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 0 and -1.25 is 0.394.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 0 and -1.25 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -1.25 for X value1 and then the larger value 0 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 2

Therefore, P(−1.25<z<0)=0.394.

Conclusion:

The area under the standard normal distribution curve for z lies between 0 and -1.25 is 0.394.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

To find: The area under the standard normal distribution curve for z lies between 0 and

–1.25. That is, P(−1.25<z<0).

Answer 20

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 0 and -1.25 is 0.394.

Answer 21

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 0 and -1.25 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -1.25 for X value1 and then the larger value 0 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 2

Therefore, P(−1.25<z<0)=0.394.

Conclusion:

The area under the standard normal distribution curve for z lies between 0 and -1.25 is 0.394.

Answer 22

(c)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 1.56 and 1.96. That is, P(1.56<z<1.96).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 1.56 and 1.96 is 0.0344.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 1.56 and 1.96 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value 1.56 for X value1 and then the larger value 1.96 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 3 .

Therefore, P(1.56<z<1.96)=0.0344.

Conclusion:

The area under the standard normal distribution curve for z lies between 1.56 and 1.96 is 0.0344.

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

To find: The area under the standard normal distribution curve for z lies between 1.56 and 1.96. That is, P(1.56<z<1.96).

Answer 27

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 1.56 and 1.96 is 0.0344.

Answer 28

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 1.56 and 1.96 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value 1.56 for X value1 and then the larger value 1.96 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 3 .

Therefore, P(1.56<z<1.96)=0.0344.

Conclusion:

The area under the standard normal distribution curve for z lies between 1.56 and 1.96 is 0.0344.

Answer 29

(d)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between -1.20 and –2.25. That is, P(−2.25<z<−1.20).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between -1.20 and -2.25 is 0.103.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between -1.20 and -2.25 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -2.25 for X value1 and then the larger value -1.20 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 4

Therefore, P(−2.25<z<−1.20)=0.103 .

Conclusion:

The area under the standard normal distribution curve for z lies between -1.20 and -2.25 is 0.103.

Answer 30

(d)

Expert Solution

Answer 31

(d)

Expert Solution

Answer 32

Expert Solution

Answer 33

To determine

To find: The area under the standard normal distribution curve for z lies between -1.20 and –2.25. That is, P(−2.25<z<−1.20).

Answer 34

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between -1.20 and -2.25 is 0.103.

Answer 35

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between -1.20 and -2.25 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -2.25 for X value1 and then the larger value -1.20 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 4

Therefore, P(−2.25<z<−1.20)=0.103 .

Conclusion:

The area under the standard normal distribution curve for z lies between -1.20 and -2.25 is 0.103.

Answer 36

(e)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between -0.06 and 0.73. That is, P(−0.06<z<0.73).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between -0.06 and 0.73 is 0.291.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between -0.06 and 0.73 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -0.06 for X value1 and then the larger value 0.73 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 5 .

Therefore, P(−0.06<z<0.73)=0.291

Conclusion:

The area under the standard normal distribution curve for z lies between -0.06 and 0.73 is 0.291.

Answer 37

(e)

Expert Solution

Answer 38

(e)

Expert Solution

Answer 39

Expert Solution

Answer 40

To determine

To find: The area under the standard normal distribution curve for z lies between -0.06 and 0.73. That is, P(−0.06<z<0.73).

Answer 41

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between -0.06 and 0.73 is 0.291.

Answer 42

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between -0.06 and 0.73 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -0.06 for X value1 and then the larger value 0.73 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 5 .

Therefore, P(−0.06<z<0.73)=0.291

Conclusion:

The area under the standard normal distribution curve for z lies between -0.06 and 0.73 is 0.291.

Answer 43

(f)

Expert Solution

To determine

To find: The area under the standard normal distribution curve for z lies between 1.10 and -1.80. That is, P(−1.80<z<1.10).

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 1.10 and -1.80 is 0.828.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 1.10 and -1.80 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -1.80 for X value1 and then the larger value 1.10 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 6

Therefore, P(−1.80<z<1.10)=0.828.

Conclusion:

The area under the standard normal distribution curve for z lies between 1.10 and -1.80 is 0.828.

Answer 44

(f)

Expert Solution

Answer 45

(f)

Expert Solution

Answer 46

Expert Solution

Answer 47

To determine

To find: The area under the standard normal distribution curve for z lies between 1.10 and -1.80. That is, P(−1.80<z<1.10).

Answer 48

Answer to Problem 18CQ

The area under the standard normal distribution curve for z lies between 1.10 and -1.80 is 0.828.

Answer 49

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve between 1.10 and -1.80 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Middle.
Type in the smaller value -1.80 for X value1 and then the larger value 1.10 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 6

Therefore, P(−1.80<z<1.10)=0.828.

Conclusion:

The area under the standard normal distribution curve for z lies between 1.10 and -1.80 is 0.828.

Answer 50

(g)

Expert Solution

To determine

To find: The area under the standard normal curve to the right of z=1.75.

Answer to Problem 18CQ

The area under the standard normal curve to the right of z=1.75 is 0.0401.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the right of 1.75 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Right Trail.
Type in the Z value of 1.75 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 7

Therefore, P(z>1.75)=0.0401.

Conclusion:

The area under the standard normal curve to the right of z=1.75 is 0.0401.

Answer 51

(g)

Expert Solution

Answer 52

(g)

Expert Solution

Answer 53

Expert Solution

Answer 54

To determine

To find: The area under the standard normal curve to the right of z=1.75.

Answer 55

Answer to Problem 18CQ

The area under the standard normal curve to the right of z=1.75 is 0.0401.

Answer 56

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the right of 1.75 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Right Trail.
Type in the Z value of 1.75 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 7

Therefore, P(z>1.75)=0.0401.

Conclusion:

The area under the standard normal curve to the right of z=1.75 is 0.0401.

Answer 57

(h)

Expert Solution

To determine

To find: The area under the standard normal curve to the right of z=−1.28.

Answer to Problem 18CQ

The area under the standard normal curve to the right of z=−1.28 is 0.8997.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the right of -1.28 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Right Trail.
Type in the Z value of -1.28 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 8

Therefore, P(z>−1.28)=0.8997

Conclusion:

The area under the standard normal curve to the right of z=−1.28 is 0.8997.

Answer 58

(h)

Expert Solution

Answer 59

(h)

Expert Solution

Answer 60

Expert Solution

Answer 61

To determine

To find: The area under the standard normal curve to the right of z=−1.28.

Answer 62

Answer to Problem 18CQ

The area under the standard normal curve to the right of z=−1.28 is 0.8997.

Answer 63

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the right of -1.28 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Right Trail.
Type in the Z value of -1.28 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 8

Therefore, P(z>−1.28)=0.8997

Conclusion:

The area under the standard normal curve to the right of z=−1.28 is 0.8997.

Answer 64

(i)

Expert Solution

To determine

To find: The area under the standard normal curve to the left of z=−2.12.

Answer to Problem 18CQ

The area under the standard normal curve to the left of z=−2.12 is 0.0170.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the left of -2.12 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Left Trail.
Type in the Z value of -2.12 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 9

Therefore, P(z<−2.12)=0.0170.

Conclusion:

The area under the standard normal curve to the left of z=−2.12 is 0.0170.

Answer 65

(i)

Expert Solution

Answer 66

(i)

Expert Solution

Answer 67

Expert Solution

Answer 68

To determine

To find: The area under the standard normal curve to the left of z=−2.12.

Answer 69

Answer to Problem 18CQ

The area under the standard normal curve to the left of z=−2.12 is 0.0170.

Answer 70

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the left of -2.12 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Left Trail.
Type in the Z value of -2.12 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 9

Therefore, P(z<−2.12)=0.0170.

Conclusion:

The area under the standard normal curve to the left of z=−2.12 is 0.0170.

Answer 71

(j)

Expert Solution

To determine

To find: The area under the standard normal curve to the left of z=1.36.

Answer to Problem 18CQ

The area under the standard normal curve to the left of z=1.36 is 0.913.

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the left of 1.36 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Left Trail.
Type in the Z value of 1.36 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 10

Therefore, P(z<1.36)=0.913.

Conclusion:

The area under the standard normal curve to the left of z=1.36 is 0.913.

Answer 72

(j)

Expert Solution

Answer 73

(j)

Expert Solution

Answer 74

Expert Solution

Answer 75

To determine

To find: The area under the standard normal curve to the left of z=1.36.

Answer 76

Answer to Problem 18CQ

The area under the standard normal curve to the left of z=1.36 is 0.913.

Answer 77

Explanation of Solution

Calculation:

Software procedure:

Use Minitab; find the area under the normal curve to the left of 1.36 with the help of following instructions:

Choose Graph > Probability Distribution Plot choose View Probability> OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Click the Shaded Area tab.
Click the picture for Left Trail.
Type in the Z value of 1.36 and click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 18CQ , additional homework tip 10

Therefore, P(z<1.36)=0.913.

Conclusion:

The area under the standard normal curve to the left of z=1.36 is 0.913.

Answer 78

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