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Chapter 7: Q. 64 (page 480)

The distribution of grade point average for students at a large high school is skewed to the left with a mean of 3.53 and a standard deviation of 1.02.

a. Describe the shape of the sampling distribution of x炉 for SRSs of size n = 4 from the population of students at this high school. Justify your answer.

b. Describe the shape of the sampling distribution of x炉 for SRSs of size n = 50 from the Page Number: 480 population of students at this high school. Justify your answer.

Short Answer

Expert verified

a. The sample mean's sampling distribution is skewed to the left.

b. The sampling distribution of the sample mean is approximately normal.

Step by step solution

01

Part (a) : Step 1 : Given information 

Given :

Mean :3.53

Standard deviation :1.02.

Size n=4

02

Part (a) : Step 2 : Simplification 

The distribution of the population is skewed to the left.

n=4

Theorem of the center limit: The sampling distribution of the sample mean x is roughly normal if the sample size is 30or greater. The central limit theorem cannot be applied since the sample size of four is less than thirty. The sample mean's sampling distribution has the same shape as the population distribution in this example, hence the sample mean's sampling distribution is skewed to the left.

03

Part (b) : Step 1 : Given information 

Given :

Mean :3.53

Standard deviation : 1.02.

Sizen=50

04

Part (b) : Step 2 : Simplification 

The distribution of the population is skewed to the left.

n=50people

Theorem of the center limit: The sampling distribution of the sample mean is roughly normal if the sample size is 30or greater. Because the sample size of 50is greater than 30, the central limit theorem can be used, and the sampling distribution of the sample mean is approximately normal.

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