New Residences The average number of moves a person makes in his or her lifetime is 12. If the standard deviation is 3.2, find the probability that the mean of a sample of 36 people is a . Less than 10 b . Greater than 10 c . Betw e en 11 and 12

Question

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Answer 1

Textbook Question

Chapter 6.3, Problem 9E

New Residences The average number of moves a person makes in his or her lifetime is 12. If the standard deviation is 3.2, find the probability that the mean of a sample of 36 people is

a. Less than 10

b. Greater than 10

c. Between 11 and 12

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 obtain: The probability that a random sample of 36 people is less than 10.

Answer to Problem 9E

The probability that a random sample of 36 people is less than 10 is 0.00009.

Explanation of Solution

Given info:

Average number of moves a person makes in his or her lifetime is μ=12 , standard deviation of number of moves a person makes in his or her lifetime is σ=3.2 and the sample size is n=36 .

Calculations:

The random variable x represents number of moves of a person in his/her lifetime.

The notation X¯ represents the mean number of moves of a person in his/her lifetime

The formula for finding the z score using central limit theorem is,

z=X¯−μσn

Substitute 10 for X¯ , 12 for μ , 3.2 for σ and 36 for n

z=(10−12)3.236=−3.75

The probability that the mean of the selected sample will be less than 10 moves represents the area to the left of 3.75.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

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.
Choose X value and Left Tail for the region of the curve to shade.
Enter the X value as –3.75.
Click OK.
Output using the MINITAB software is given below:

From MINITAB output, the probability that a random sample of 36 people is less than 10 is 0.00009.

b.

Expert Solution

To determine

To obtain: The probability that a random sample of 36 people is greater than 10.

Answer to Problem 9E

Probability will be 0.9999.

Explanation of Solution

Calculations:

The formula for finding the z score using central limit theorem is,

z=X¯−μσn

Substitute 10 for X¯ , 12 for μ , 3.2 for σ and 36 for n

z=(10−12)3.236=−3.75

The probability that a random sample of 36 people greater than 10 represents the area to the right of –3.75.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

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.
Choose X value and Right Tail for the region of the curve to shade.
Enter the X value as –3.75.
Click OK.
Output using the MINITAB software is given below:
From MINITAB output, the probability that a random sample of 36 people greater than 10 is 0.9999.

c.

Expert Solution

To determine

The probability that a random sample of 36 people between 11 and 12.

Answer to Problem 9E

The probability that a random sample of 36 people is between 11 and 12 is 0.4699.

Explanation of Solution

Calculations:

The formula for finding the z score using central limit theorem is,

z=X¯−μσn

Substitute 11 and 12 for X¯1 and X¯2 , 12 for μ , 3.2 for σ and 36 for n

z1=(11−12)3.236 =−1.88z2=(12−12)3.236 =0

The probability that a random sample of 36 people is between 11 and 12 represents area between the value −1.88 and 0.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

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.
Choose X value and Middle for the region of the curve to shade.
Enter the X value 1 as –1.88 and X value 2 as 0.
Click OK.
Output using the MINITAB software is given below:

ELEMENTARY STATISTICS: STEP BY STEP- ALE, Chapter 6.3, Problem 9E , additional homework tip 3

From MINITAB output, the probability that a random sample of 36 people is between 11 and 12 is 0.4699.

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Answer 2

Textbook Question

Chapter 6.3, Problem 9E

New Residences The average number of moves a person makes in his or her lifetime is 12. If the standard deviation is 3.2, find the probability that the mean of a sample of 36 people is

a. Less than 10

b. Greater than 10

c. Between 11 and 12

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 obtain: The probability that a random sample of 36 people is less than 10.

Answer to Problem 9E

The probability that a random sample of 36 people is less than 10 is 0.00009.

Explanation of Solution

Given info:

Average number of moves a person makes in his or her lifetime is μ=12 , standard deviation of number of moves a person makes in his or her lifetime is σ=3.2 and the sample size is n=36 .

Calculations:

The random variable x represents number of moves of a person in his/her lifetime.

The notation X¯ represents the mean number of moves of a person in his/her lifetime

The formula for finding the z score using central limit theorem is,

z=X¯−μσn

Substitute 10 for X¯ , 12 for μ , 3.2 for σ and 36 for n

z=(10−12)3.236=−3.75

The probability that the mean of the selected sample will be less than 10 moves represents the area to the left of 3.75.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

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.
Choose X value and Left Tail for the region of the curve to shade.
Enter the X value as –3.75.
Click OK.
Output using the MINITAB software is given below:

From MINITAB output, the probability that a random sample of 36 people is less than 10 is 0.00009.

b.

Expert Solution

To determine

To obtain: The probability that a random sample of 36 people is greater than 10.

Answer to Problem 9E

Probability will be 0.9999.

Explanation of Solution

Calculations:

The formula for finding the z score using central limit theorem is,

z=X¯−μσn

Substitute 10 for X¯ , 12 for μ , 3.2 for σ and 36 for n

z=(10−12)3.236=−3.75

The probability that a random sample of 36 people greater than 10 represents the area to the right of –3.75.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

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.
Choose X value and Right Tail for the region of the curve to shade.
Enter the X value as –3.75.
Click OK.
Output using the MINITAB software is given below:
From MINITAB output, the probability that a random sample of 36 people greater than 10 is 0.9999.

c.

Expert Solution

To determine

The probability that a random sample of 36 people between 11 and 12.

Answer to Problem 9E

The probability that a random sample of 36 people is between 11 and 12 is 0.4699.

Explanation of Solution

Calculations:

The formula for finding the z score using central limit theorem is,

z=X¯−μσn

Substitute 11 and 12 for X¯1 and X¯2 , 12 for μ , 3.2 for σ and 36 for n

z1=(11−12)3.236 =−1.88z2=(12−12)3.236 =0

The probability that a random sample of 36 people is between 11 and 12 represents area between the value −1.88 and 0.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

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.
Choose X value and Middle for the region of the curve to shade.
Enter the X value 1 as –1.88 and X value 2 as 0.
Click OK.
Output using the MINITAB software is given below:

ELEMENTARY STATISTICS: STEP BY STEP- ALE, Chapter 6.3, Problem 9E , additional homework tip 3

From MINITAB output, the probability that a random sample of 36 people is between 11 and 12 is 0.4699.

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

Answer 3

Textbook Question

Chapter 6.3, Problem 9E

New Residences The average number of moves a person makes in his or her lifetime is 12. If the standard deviation is 3.2, find the probability that the mean of a sample of 36 people is

a. Less than 10

b. Greater than 10

c. Between 11 and 12

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 obtain: The probability that a random sample of 36 people is less than 10.

Answer to Problem 9E

The probability that a random sample of 36 people is less than 10 is 0.00009.

Explanation of Solution

Given info:

Average number of moves a person makes in his or her lifetime is μ=12 , standard deviation of number of moves a person makes in his or her lifetime is σ=3.2 and the sample size is n=36 .

Calculations:

The random variable x represents number of moves of a person in his/her lifetime.

The notation X¯ represents the mean number of moves of a person in his/her lifetime

The formula for finding the z score using central limit theorem is,

z=X¯−μσn

Substitute 10 for X¯ , 12 for μ , 3.2 for σ and 36 for n

z=(10−12)3.236=−3.75

The probability that the mean of the selected sample will be less than 10 moves represents the area to the left of 3.75.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

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.
Choose X value and Left Tail for the region of the curve to shade.
Enter the X value as –3.75.
Click OK.
Output using the MINITAB software is given below:

From MINITAB output, the probability that a random sample of 36 people is less than 10 is 0.00009.

b.

Expert Solution

To determine

To obtain: The probability that a random sample of 36 people is greater than 10.

Answer to Problem 9E

Probability will be 0.9999.

Explanation of Solution

Calculations:

The formula for finding the z score using central limit theorem is,

z=X¯−μσn

Substitute 10 for X¯ , 12 for μ , 3.2 for σ and 36 for n

z=(10−12)3.236=−3.75

The probability that a random sample of 36 people greater than 10 represents the area to the right of –3.75.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

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.
Choose X value and Right Tail for the region of the curve to shade.
Enter the X value as –3.75.
Click OK.
Output using the MINITAB software is given below:
From MINITAB output, the probability that a random sample of 36 people greater than 10 is 0.9999.

c.

Expert Solution

To determine

The probability that a random sample of 36 people between 11 and 12.

Answer to Problem 9E

The probability that a random sample of 36 people is between 11 and 12 is 0.4699.

Explanation of Solution

Calculations:

The formula for finding the z score using central limit theorem is,

z=X¯−μσn

Substitute 11 and 12 for X¯1 and X¯2 , 12 for μ , 3.2 for σ and 36 for n

z1=(11−12)3.236 =−1.88z2=(12−12)3.236 =0

The probability that a random sample of 36 people is between 11 and 12 represents area between the value −1.88 and 0.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

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.
Choose X value and Middle for the region of the curve to shade.
Enter the X value 1 as –1.88 and X value 2 as 0.
Click OK.
Output using the MINITAB software is given below:

ELEMENTARY STATISTICS: STEP BY STEP- ALE, Chapter 6.3, Problem 9E , additional homework tip 3

From MINITAB output, the probability that a random sample of 36 people is between 11 and 12 is 0.4699.

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

Answer 4

Textbook Question

Chapter 6.3, Problem 9E

New Residences The average number of moves a person makes in his or her lifetime is 12. If the standard deviation is 3.2, find the probability that the mean of a sample of 36 people is

a. Less than 10

b. Greater than 10

c. Between 11 and 12

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 obtain: The probability that a random sample of 36 people is less than 10.

Answer to Problem 9E

The probability that a random sample of 36 people is less than 10 is 0.00009.

Explanation of Solution

Given info:

Average number of moves a person makes in his or her lifetime is μ=12 , standard deviation of number of moves a person makes in his or her lifetime is σ=3.2 and the sample size is n=36 .

Calculations:

The random variable x represents number of moves of a person in his/her lifetime.

The notation X¯ represents the mean number of moves of a person in his/her lifetime

The formula for finding the z score using central limit theorem is,

z=X¯−μσn

Substitute 10 for X¯ , 12 for μ , 3.2 for σ and 36 for n

z=(10−12)3.236=−3.75

The probability that the mean of the selected sample will be less than 10 moves represents the area to the left of 3.75.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

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.
Choose X value and Left Tail for the region of the curve to shade.
Enter the X value as –3.75.
Click OK.
Output using the MINITAB software is given below:

From MINITAB output, the probability that a random sample of 36 people is less than 10 is 0.00009.

b.

Expert Solution

To determine

To obtain: The probability that a random sample of 36 people is greater than 10.

Answer to Problem 9E

Probability will be 0.9999.

Explanation of Solution

Calculations:

The formula for finding the z score using central limit theorem is,

z=X¯−μσn

Substitute 10 for X¯ , 12 for μ , 3.2 for σ and 36 for n

z=(10−12)3.236=−3.75

The probability that a random sample of 36 people greater than 10 represents the area to the right of –3.75.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

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.
Choose X value and Right Tail for the region of the curve to shade.
Enter the X value as –3.75.
Click OK.
Output using the MINITAB software is given below:
From MINITAB output, the probability that a random sample of 36 people greater than 10 is 0.9999.

c.

Expert Solution

To determine

The probability that a random sample of 36 people between 11 and 12.

Answer to Problem 9E

The probability that a random sample of 36 people is between 11 and 12 is 0.4699.

Explanation of Solution

Calculations:

The formula for finding the z score using central limit theorem is,

z=X¯−μσn

Substitute 11 and 12 for X¯1 and X¯2 , 12 for μ , 3.2 for σ and 36 for n

z1=(11−12)3.236 =−1.88z2=(12−12)3.236 =0

The probability that a random sample of 36 people is between 11 and 12 represents area between the value −1.88 and 0.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

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.
Choose X value and Middle for the region of the curve to shade.
Enter the X value 1 as –1.88 and X value 2 as 0.
Click OK.
Output using the MINITAB software is given below:

ELEMENTARY STATISTICS: STEP BY STEP- ALE, Chapter 6.3, Problem 9E , additional homework tip 3

From MINITAB output, the probability that a random sample of 36 people is between 11 and 12 is 0.4699.

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

Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

a.

Expert Solution

To determine

To obtain: The probability that a random sample of 36 people is less than 10.

Answer to Problem 9E

The probability that a random sample of 36 people is less than 10 is 0.00009.

Explanation of Solution

Given info:

Average number of moves a person makes in his or her lifetime is μ=12 , standard deviation of number of moves a person makes in his or her lifetime is σ=3.2 and the sample size is n=36 .

Calculations:

The random variable x represents number of moves of a person in his/her lifetime.

The notation X¯ represents the mean number of moves of a person in his/her lifetime

The formula for finding the z score using central limit theorem is,

z=X¯−μσn

Substitute 10 for X¯ , 12 for μ , 3.2 for σ and 36 for n

z=(10−12)3.236=−3.75

The probability that the mean of the selected sample will be less than 10 moves represents the area to the left of 3.75.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

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.
Choose X value and Left Tail for the region of the curve to shade.
Enter the X value as –3.75.
Click OK.
Output using the MINITAB software is given below:

From MINITAB output, the probability that a random sample of 36 people is less than 10 is 0.00009.

b.

Expert Solution

To determine

To obtain: The probability that a random sample of 36 people is greater than 10.

Answer to Problem 9E

Probability will be 0.9999.

Explanation of Solution

Calculations:

The formula for finding the z score using central limit theorem is,

z=X¯−μσn

Substitute 10 for X¯ , 12 for μ , 3.2 for σ and 36 for n

z=(10−12)3.236=−3.75

The probability that a random sample of 36 people greater than 10 represents the area to the right of –3.75.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

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.
Choose X value and Right Tail for the region of the curve to shade.
Enter the X value as –3.75.
Click OK.
Output using the MINITAB software is given below:
From MINITAB output, the probability that a random sample of 36 people greater than 10 is 0.9999.

c.

Expert Solution

To determine

The probability that a random sample of 36 people between 11 and 12.

Answer to Problem 9E

The probability that a random sample of 36 people is between 11 and 12 is 0.4699.

Explanation of Solution

Calculations:

The formula for finding the z score using central limit theorem is,

z=X¯−μσn

Substitute 11 and 12 for X¯1 and X¯2 , 12 for μ , 3.2 for σ and 36 for n

z1=(11−12)3.236 =−1.88z2=(12−12)3.236 =0

The probability that a random sample of 36 people is between 11 and 12 represents area between the value −1.88 and 0.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

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.
Choose X value and Middle for the region of the curve to shade.
Enter the X value 1 as –1.88 and X value 2 as 0.
Click OK.
Output using the MINITAB software is given below:

ELEMENTARY STATISTICS: STEP BY STEP- ALE, Chapter 6.3, Problem 9E , additional homework tip 3

From MINITAB output, the probability that a random sample of 36 people is between 11 and 12 is 0.4699.

Answer 8

a.

Expert Solution

To determine

To obtain: The probability that a random sample of 36 people is less than 10.

Answer to Problem 9E

The probability that a random sample of 36 people is less than 10 is 0.00009.

Explanation of Solution

Given info:

Average number of moves a person makes in his or her lifetime is μ=12 , standard deviation of number of moves a person makes in his or her lifetime is σ=3.2 and the sample size is n=36 .

Calculations:

The random variable x represents number of moves of a person in his/her lifetime.

The notation X¯ represents the mean number of moves of a person in his/her lifetime

The formula for finding the z score using central limit theorem is,

z=X¯−μσn

Substitute 10 for X¯ , 12 for μ , 3.2 for σ and 36 for n

z=(10−12)3.236=−3.75

The probability that the mean of the selected sample will be less than 10 moves represents the area to the left of 3.75.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

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.
Choose X value and Left Tail for the region of the curve to shade.
Enter the X value as –3.75.
Click OK.
Output using the MINITAB software is given below:

From MINITAB output, the probability that a random sample of 36 people is less than 10 is 0.00009.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

To obtain: The probability that a random sample of 36 people is less than 10.

Answer 13

Answer to Problem 9E

The probability that a random sample of 36 people is less than 10 is 0.00009.

Answer 14

Explanation of Solution

Given info:

Average number of moves a person makes in his or her lifetime is μ=12 , standard deviation of number of moves a person makes in his or her lifetime is σ=3.2 and the sample size is n=36 .

Calculations:

The random variable x represents number of moves of a person in his/her lifetime.

The notation X¯ represents the mean number of moves of a person in his/her lifetime

The formula for finding the z score using central limit theorem is,

z=X¯−μσn

Substitute 10 for X¯ , 12 for μ , 3.2 for σ and 36 for n

z=(10−12)3.236=−3.75

The probability that the mean of the selected sample will be less than 10 moves represents the area to the left of 3.75.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

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.
Choose X value and Left Tail for the region of the curve to shade.
Enter the X value as –3.75.
Click OK.
Output using the MINITAB software is given below:

From MINITAB output, the probability that a random sample of 36 people is less than 10 is 0.00009.

Answer 15

b.

Expert Solution

To determine

To obtain: The probability that a random sample of 36 people is greater than 10.

Answer to Problem 9E

Probability will be 0.9999.

Explanation of Solution

Calculations:

The formula for finding the z score using central limit theorem is,

z=X¯−μσn

Substitute 10 for X¯ , 12 for μ , 3.2 for σ and 36 for n

z=(10−12)3.236=−3.75

The probability that a random sample of 36 people greater than 10 represents the area to the right of –3.75.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

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.
Choose X value and Right Tail for the region of the curve to shade.
Enter the X value as –3.75.
Click OK.
Output using the MINITAB software is given below:
From MINITAB output, the probability that a random sample of 36 people greater than 10 is 0.9999.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

To obtain: The probability that a random sample of 36 people is greater than 10.

Answer 20

Answer to Problem 9E

Probability will be 0.9999.

Answer 21

Explanation of Solution

Calculations:

The formula for finding the z score using central limit theorem is,

z=X¯−μσn

Substitute 10 for X¯ , 12 for μ , 3.2 for σ and 36 for n

z=(10−12)3.236=−3.75

The probability that a random sample of 36 people greater than 10 represents the area to the right of –3.75.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

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.
Choose X value and Right Tail for the region of the curve to shade.
Enter the X value as –3.75.
Click OK.
Output using the MINITAB software is given below:
From MINITAB output, the probability that a random sample of 36 people greater than 10 is 0.9999.

Answer 22

c.

Expert Solution

To determine

The probability that a random sample of 36 people between 11 and 12.

Answer to Problem 9E

The probability that a random sample of 36 people is between 11 and 12 is 0.4699.

Explanation of Solution

Calculations:

The formula for finding the z score using central limit theorem is,

z=X¯−μσn

Substitute 11 and 12 for X¯1 and X¯2 , 12 for μ , 3.2 for σ and 36 for n

z1=(11−12)3.236 =−1.88z2=(12−12)3.236 =0

The probability that a random sample of 36 people is between 11 and 12 represents area between the value −1.88 and 0.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

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.
Choose X value and Middle for the region of the curve to shade.
Enter the X value 1 as –1.88 and X value 2 as 0.
Click OK.
Output using the MINITAB software is given below:

ELEMENTARY STATISTICS: STEP BY STEP- ALE, Chapter 6.3, Problem 9E , additional homework tip 3

From MINITAB output, the probability that a random sample of 36 people is between 11 and 12 is 0.4699.

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

The probability that a random sample of 36 people between 11 and 12.

Answer 27

Answer to Problem 9E

The probability that a random sample of 36 people is between 11 and 12 is 0.4699.

Answer 28

Explanation of Solution

Calculations:

The formula for finding the z score using central limit theorem is,

z=X¯−μσn

Substitute 11 and 12 for X¯1 and X¯2 , 12 for μ , 3.2 for σ and 36 for n

z1=(11−12)3.236 =−1.88z2=(12−12)3.236 =0

The probability that a random sample of 36 people is between 11 and 12 represents area between the value −1.88 and 0.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

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.
Choose X value and Middle for the region of the curve to shade.
Enter the X value 1 as –1.88 and X value 2 as 0.
Click OK.
Output using the MINITAB software is given below: