The distribution of scores on a test for a particular class

The distribution of scores on a test for a particular class is skewed to the right. The professor wants to predict the maximum score and understand the distribution of the sample maximum. She simulates the distribution of the maximum of the test for 38 different tests (with n = 5). The histogram to the right shows a simulated sampling distribution of the sample maximum from these tests. Complete parts a) and b) below. Would a Normal model be a useful model for this sampling distribution? Explain. The mean of this distribution is 46.8 and the SD is 3.5. Would you expect about 99.7% of the samples to have their maximums within 10.5 of 46.8? Why or why not?

Solution

a.) B. The sampling distribution is skewed to the right so the normal mode would not be useful for this sampling distribution.

b.) C. No. The values show too much variation to apply 68-95-99.7 rule