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Standard Distribution and probability

Assume that the population of heights of male college students is approximately normally distributed with mean m of 68 inches and standard deviation s of 3.75 inches. A random sample of 16 heights is obtained.
d. Find the mean and standard error of the xbar distribution.
e. Find P (xbar > 70)
f. Find P ( xbar < 67)
I know that I am working with sampling distributions of sample means.

Solution Preview

The Mean of the population = Mean of the sample
Thus the mean of the random sample of 16 heights will be 68 inches.

Standard deviation of sample = Standard deviation of population / ...

Solution Summary

The solution finds the mean and standard distribution of the given scenario and then estimates probailities for certain conditions.