# the random heights of north american women

The heights of North American women are normally distributed with a mean of 64 inches and a standard deviation of 2 inches. A random sample of four women is selected. What is the probability that the sample mean height is greater than 66 inches?

What is the formula for going about this problem? I am searching through my textbook, but cant seem to find out how to solve this. The random sample of four is the part that is throwing me off.

• If x has a normal distribution, what can we say about the distribution of $\bar{x}$? – Brad S. Mar 26 '14 at 0:28

Say that your four sampled heights are $X_1,X_2,X_3,X_4$. These are independent random variables that are normally distributed with mean $64$ and standard deviation $2$.
The question is then asking you for $$P\left(\frac{X_1+X_2+X_3+X_4}{4}\geq66\right).$$