IQ scores are normally distributed with a mean of 95 and a standard deviation of 18 . Assume that many samples of size n are taken from a large population of people and the mean IQ score is computed for each sample.

a. If the sample size is n= 64, find the mean and standard deviation of the distribution of sample means.

The mean of the distribution of sample means is

?.

The standard deviation of the distribution of sample means is

?.

(Type an integer or decimal rounded to the nearest tenth as needed.)

b. If the sample size is n, find the mean and standard deviation of the distribution of sample means.

The mean of the distribution of sample means is

?.

The standard deviation of the distribution of sample means is

enter your response here.

(Type an integer or decimal rounded to the nearest tenth as needed.)

c. Why is the standard deviation in part a different from the standard deviation in part b? Choose the correct answer below.

A.

With larger sample sizes (as in part b), the means tend to be further apart, so they have more variation, which results in a bigger standard deviation.

B.

With smaller sample sizes (as in part a), the means tend to be further apart, so they have more variation, which results in a smaller standard deviation.

C.

With smaller sample sizes (as in part a), the means tend to be closer together, so they have less variation, which results in a smaller standard deviation.

D.

With larger sample sizes (as in part b), the means tend to be closer together, so they have less variation, which results in a smaller standard deviation.