According to a 2018 report from the Center for Disease Control and Prevention (CDC), the average heights of adult women and men were 161.5 cm and 175.4 cm, respectively. Assume the heights follow, each, a Normal distribution with the given average and both have a standard deviation of 6.4 cm. Let X be the height of a random woman and let X be the height of a random man. a. What is P(X > 180), i.e., the man is over 180 cm? b. Let Y = X2 + X. Is Y normal? What are the expected value and variance of Y? c. What is the probability that the random man and woman have an average height over 180 cm? (Hint: This would require the sum of their heights to be over 360 cm.) d. Let D = X2 - X. Is D normal? Obtain ED and VarD. e. What is the probability that the random man is shorter than the random woman?