At the end of the spring semester, the Dean of Students sent a survey to the entire freshman class. One question asked the students how much weight they had gained or lost since the beginning of the school year. The average was a gain of μ = 9 pounds with a standard deviation of σ = 6. The distribution of scores was approximately normal. A sample of n = 4 students is selected and the average weight change is computed for the sample.

a. What is the probability that the sample mean will be greater than M > 10 pounds? In symbols, what is p(M > 10)?

b. Of all of the possible samples, what proportion will show an average weight loss? In symbols, what is p(M < 0)?

c. What is the probability that the sample mean will be a gain of between M = 9 and M = 12 pounds? In symbols, what is p(9 < M < 12)?