Heights of men in America have a normal distribution with a mean of 69.5 9nches and a standard deviation of 3 inches. Perform the following calculations.. Let X represent the mean height of a random sample of n American adult men. Find n if P(68.52 < X <70.48) = .95.? If 100 American men are chosen at random, find the probability that at least 25 of them are shorter than 68 inches. Hint, let Y be the number of Americans shorter than 68, then Y is binomial. Find the probability using a normal approximation?