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QUESTION

IQ scores are normally distributed with a mean of 95 and a standard deviation of 17.

IQ scores are normally distributed with a mean of 95 and a standard deviation of 17.

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 nequals=36,

A. 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 _____

b. If the sample size is nequals=100,

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 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 closer​ together, so they have less​ 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 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.