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

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)?

© BrainMass Inc. brainmass.com October 10, 2019, 5:02 am ad1c9bdddfhttps://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.