An intelligence quotient, or IQ, is a measurement of intelligence derived from a standardized test, such as the Stanford Binet IQ test. Scores on this test are approximately normally distributed with a mean score of 100 and a standard deviation of 15. What is the sampling distribution of the sample mean for a sample of size n = 9?

Approach The problem asks us to determine the shape, center, and spread of the distribution of the sample mean. Remember, the sampling distribution of the sample mean would be the distribution of all possible sample means of size n = 9. To get a sense of this distribution, use Minitab to simulate obtaining 1000 samples of size n = 9 by randomly generating 1000 rows of IQs over 9 columns. Each row represents a random sample of size 9. For each of the 1000 samples (the 1000 rows), we determine the mean IQ score. Draw a histogram to gauge the shape of the distribution of the sample mean, determine the mean of the 1000 sample means to approximate the mean of the sampling distribution, and determine the standard deviation of the 1000 sample means to approximate the standard deviation of the sampling distribution.