Problem $2.$ A Motel has $16$ bedrooms. From past experience, the manager knows that

$20\%$ of the people who make room reservations don$$t show up$.$ 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.

$($Note: Show your derivations and calculate by hand without MINITAB to get credit.$)$

$($a$)$ What is the expected number of customers that will show up$?$

$($b$)$What is the expected value of the compensation that the motel must pay?