# Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15

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?

What if the size for each sample were increased to 20? Would a sample mean of 115 or more be considered unusual? Why or why not?

What about if we have:

The mean of a sample of 20 is 105 or more? Is this an unusual event looking at this information? Why is the Central Limit Theorem used? Explain!

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