Suppose that the height of a typical American female is normally distributed with μ = 64 inches and σ = 4 inches. We observe the height of 500 American females.
a. What is the probability that fewer than 35 of the 500 women will be less than 58 inches tall?
b. Let X be the number of the 500 women who are less than 58 inches tall. Find the mean and standard deviation of X.