(10 points) The heights of a randomly chosen male American and of a randomly chosen female American (in inches) can be described by independent normal random variables X and Y, respectively. Here, X ~ /(70, 32) and Y ~ /(64.5, 2.53). a) What is the probability that a randomly chosen male is at least three inches taller than a randomly chosen female? b) What is the probability that a randomly chosen male is more than 15% taller than a randomly chosen female