Suppose that the height of a typical American female is normally distributed with = 64 inches

Question:

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.

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