Reference no: EM132465159

IQ scores are normally distributed with a mean of 100 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 =81find 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

b. If the sample size is n=144 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

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

A. 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.

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 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.

D. 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.