Assume that a population is normally distributed with a mean of 100 and a standard deviation...
Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not? Provide an example.
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Homework Answers
Solution:
Given: A population is normally distributed with a mean of 100 and a standard deviation of 15.
Thus Mean = 
Standard Deviation = 
Sample size = n = 3
We have to find if it is unusual for the mean of a sample of 3 to be 115 or more.
Thus find:
=..............?
Find z score:
Thus we get:
Look in z table for z = 1.7 and 0.03 and find corresponding area.
P( Z< 1.73 ) = 0.9582
Thus
Since this probability is less than 0.05 ( or 5% ) , it would be unusual for the mean of a sample of 3 to be 115 or more.
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