Please solve the following problem.

Problem 6 The heights of men in the United States are normally distributed with mean (19.1 inches and standard de viation 2.9 inches. The heights of women are normally distributed with mean ll inches and standard deviation 2.? inches. Let Jr be the average height of Ill randomly sampled men. and y be the average height of [t] randomly sampled women. {a} 1What is the distribution of .r y? {b} Using simulations in R, calculate the Monte Carlo estimates of the mean and standard deviation of the distribution of Jr y. Compare these estimates with the exact values of the mean and standard deviation. {c} What is the probability that a randomly sampled man is taller than a randomly sampled woman? Please do not answer this question by reporting a Monte Carlo estimate of this probability