Question: [30 points]

The heights of men in the United States are normally distributed with mean 69.1 inches and standard deviation 2.9 inches. The heights of women are normally distributed with mean 63.7 inches and standard deviation 2.7 inches. Let x be the average height of 100 randomly sampled men, and y be the average height of 100 randomly sampled women.

1. [10 points] What is the distribution of x - y?
2. [10 points] Using simulations in R, calculate the Monte Carlo estimates of the mean and standard deviation of the distribution of x - y. Compare these estimates with the exact values of the mean and standard deviation.
3. [10 points] 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.

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Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document