Question: A typical consumer buys a random number (X) of polo shirts when he shops at a men's clothing store. The distribution of X is given by the following probability distribution: P(X = 0) = 0.30, P(X = 1) = 0.30, P(X = 2) = 0.20, P(X = 3) = 0.10, and P(X = 4) = 0.10.
a. Find the mean and standard deviation of X.
b. Assuming that each shirt costs $35, let Y be the total amount of money (in dollars) spent by a customer when he visits this clothing store. Find the mean and standard deviation of Y.
c. Find the probability that a customer's expenditure will be more than one standard deviation above the mean expenditure level.