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# What is probability that the sample mean will be greater than M=10 pounds?

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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 a mean=9 pounds with a standard deviation=6. The distribution of scores was approximately normal. A sample of n=4 student is selected and the average weight change is computed for the sample.

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

b) Of all the possible samples, what proportion will show an average weight? 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)?

https://brainmass.com/math/probability/probability-sample-mean-greater-pound-489771

#### Solution Preview

Hi there,

Here are my explanations:

a. ...

#### Solution Summary

The expert determines the probability that the sample mean will be greater than M=10 pounds.

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