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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.
