Problem 18E

A random sample of n = 64 observations is drawn from a population with a mean equal to 20 and a standard deviation equal to 16.

a. Give the mean and standard deviation of the (repeated) sampling distribution of .

b. Describe the shape of the sampling distribution of Does your answer depend on the sample size?

c. Calculate the standard normal z-score corresponding to a value of = 15.5.

d. Calculate the standard normal z-score corresponding to =23

Solution:

Step 1 of 3:

A random sample of n=64 observations is drawn from a population with a mean equal to 20 and the standard deviation equal to 16.

- We have to find the mean and standard deviation of the sampling distribution of .
- We have to describe the shape of the sampling distribution.
- We have to calculate the standard normal Z-score corresponding to a value of =15.5.
- We have to calculate the standard normal Z-score corresponding to =23.