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1 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?
Standard deviation =15
Sample size (n) = 3
We use 95% significance level where 1-0.95=0.05/2=0.025 from tables =1.96
Formula =
Replacing the value in the formula
It would not be unusual for the mean to be 115 since it lies in between the range of 116.97 and 83.03.
* What if the size for each sample was increased to 20? Would a sample mean of 115 or more be considered unusual? Why or why not?
Mean= 100
Standard deviation= 15
Sample Size= 20
With the same significance level of 95%
The sample mean of 115 would be considered unusual since the sample mean of 115 exceeds the limit in place of 106.57 and 93.43.
* Why is the Central Limit Theorem used?
Central Limit Theorem is

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