A car dealer organizes a new promotional campaign. Buyers of new cars can return them within 2 days if they are not satisfied and get all the money paid back. The cost to the dealer for the refund is $250. The dealership estimates that 15 percent of all buyers will return the cars and get their money back. Suppose 50 cars are purchased during the campaign.

a) Calculate the probability distribution of the number of cars returned.

b) What is the probability that 5 or more cars are returned?

c) What is the probability that 10 or more cars are returned?

d) What is the probability that 25 or more cars are returned?

e) Find the mean and standard deviation of the number of cars that will be returned in exchange for the money.

f) Find the mean and standard deviation of the total costs of paying back the money for these 50 purchases.