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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 20 to be 115 or more? Why or why not?
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Answer #1

Given that a population is normally distributed with a mean of and a standard deviation of

For a sample of size n from normally distributed population, the sampling distribution of the sample mean is also normally distributed with mean and standard deviation of .

Therefore, the probability   can be obtained using the Excel formula NORMDIST (x, mean, standard deviation, 1) as below:

The probability    is very high so it cannot be unusual for the mean of sample 20 to be 115 or more.

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