# Question: At the end of the spring semester the Dean of

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 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)?

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 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)?

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