The heights of men in the US are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. The heights of women in the US are
normally distributed with a mean of 65 inches and a standard deviation of 2.5
inches. If we select 1 man and 1 woman randomly from the population the
differences (M-W) should be normal as well. Assume the heights are independent of one another. Find the mean and standard deviation of the distribution of the differences in height. Then, use it to find the probability that the difference could be less than zero, which means that the woman selected is taller than the man selected.
A. P(X < 0) = 0.1003
B. P(X < 0) = 0.1814
C. P(X < 0) = 0.8186
D. P(X < 0) = 0.8997