A Motel has 15 bedrooms. From past experience, the manager knows that on the average, 20% of the people who make room reservations don't show up. On a particular day, the manager accepts 20 reservations. If a customer with a reservation shows up and the motel has run out of rooms, it is the motel's policy to pay $100 as compensation to the customer.

a) What is the probability distribution of the compensation that the motel must pay?

b) What is the expected value and standard deviation of the compensation that the motel must pay?