Sample maximum The distribution of scores on a Statistics test for a particular class is skewed to the left.

The professor wants to predict the maximum score and so wants to understand the distribution of the sample maximum. She simulates the distribution of the maximum of the test for 30 different tests (with n = 5). The histogram below shows a simulated sampling distribution of the sample maximum from these tests.

a) Would a Normal model be a useful model for this sampling distribution? Explain.

b) The mean of this distribution is 46.3 and the SD is 3.5.
Would you expect about 95% of the samples to have their maximums within 7 of 46.3? Why or why not?

Frequency 15 10 10 5 35 40 45 Max Score 50 50