Question: At the beginning of a new term at a major university, a survey is taken at the University's book store. The survey asked 16 randomly chosen students to state the number of books they will buy in the coming term. You may assume that the number of books a student purchases per term is normally distributed with μ = 7.8 books per semester and σ = 2.9.

a) Explain how the sample mean is (exactly) distributed in this sample.

Suppose the students gave the following answers:

6 11 4 7 7 S x_i = 100

7 1 4 5 7 S (x_i -`x )² = 141.5

3 3 8 6 13 9

b) Find the probability of getting a sample mean less than or equal to the value in this sample if μ = 7.8 books per semester and σ = 2.9.

c) Based on this sample, is it likely that the population mean for the number of books bought per semester really is 7.8? Explain briefly.