Assume that a population is normally distributed with a mean

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?

Solution

Since the population is normal distributed, the sample will also be normal distributed.
(Though logically, we shouldn\'t use such a small sample size.)

Let X = mean of a sample containing 3 subjects.
X~normal(100 , 15^2 / 3)

P(X >= 115)
= P(X >= (115 - 100) / sqrt(15^2 / 3))
= P(X >= 1.732050808)
= 0.0418

Yes, it will be unusual, as there is only a 4.18% chance for that to occur.

This should be the standard answer.

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