# 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?Please provide a brief...

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?

Please provide a brief explanation with your answer.

Asked on by cbuteaux

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

Your question is not very clear, I would recommend you define what exactly you mean by "unusual." Here is my response to what I hope you want to know.

The mean of the population is 100 and it is normally distributed with a standard deviation of 15.

This means that approximately 68.2% of the population has a value that lies between 85 and 115.

As normally distributed values have an equal probability of being greater or lesser than the mean, approximately 15.9% of the population has a value greater than 115.

If by unusual, you mean a probability less than 15.9% it would be unusual for the mean of a sample of 3 to be 115 or more.

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