(Textbook, ch.5, #22). Among private universities in the United States, the mean ratio of students to professors is 35.2 (i.e. 35.2 students for each professor)with a standard deviation of 8.8.

a. What is the probability that in a random sample of 50 private universities the mean student-to-professor exceeds 38?

b. Suppose a random sample of 50 universities is selected and the observed mean student-to-professor ratio is 38.Is there evidence that the reported mean ratio actually exceeds 35.2?use alpha=0.05

c. Suppose a random sample of 50 universities is selected and the observed mean student-to-professor ratio is 38. Is there evidence that the reported mean ratio differs from 35.2? Use = 0:05.