Question

IQ scores are normally distributed with a mean of 105 and a standard deviation of 15. 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 equals= 64, find the mean and standard deviation of the distribution of sample means.

The mean of the distribution of sample means is: 105

The standard deviation of the distribution of sample means is ? (Type an integer or decimal rounded to the nearest tenth as needed.)

Answer 1

Solution: We know that the mean of the sampling distribution of the mean is the mean of the population from which the scores were sampled. Therefore, if a population has a mean , then the mean of the sampling distribution of the mean is also . While the standard deviation of the sampling distribution of the mean is the population standard deviation divided by , the sample size.

Since we know that IQ scores are normally distributed with a mean of 105 and a standard deviation of 15.

Also we are give the sample size

Therefore the standard deviation of the distribution of sample means