Example 5.6.6 Heights of Men and Women. Suppose that the heights.in inches, of the women in a certain population follow a normal distribution with mean 65 and standard deviation 1, and that the heights of the men follow a normal distribution with mean 68 and standard deviation 2. Suppose also that one woman is selected at random and, independently, one man is selected at random. We shall determine the probability that the woman will be taller than the man.