At the end of the spring semester, the Dean of Students sent a survey to the entire

Question:

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 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 µ = 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 µ = 9 and µ = 12 pounds? In symbols, what is p(9 , µ , 12)?
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...