Question: Suppose the heights of adult males in a population have a normal distribution with mean μ = 70 inches and standard deviation σ = 2.8 inches. Two unrelated men will be randomly sampled. Let X = height of the first man and Y = height of the second man.
a. Consider D = X - Y, the difference between the heights of the two men. What type of distribution will the variable D have?
b. What is the mean value for the distribution of D?
c. Assuming independence between the two men, find the standard deviation of D.
d. Determine the probability that the first man is more than 3 inches taller than the second man. That is, find P(D > 3).