On a given Philadelphia­Los Angeles flight, there are 200 seats. Suppose the ticket price is $475 on average and the number of passengers who reserve a seat but do not show up for departure is normally distributed with mean 30 and standard deviation 15. You decide to overbook the flight and estimate that the average loss from a passenger who will have to be bumped (if the number of passengers exceeds the number of seats) is $800.
a. What is the maximum number of reservations that should be accepted?
b. Suppose you allow 220 reservations. How much money do you expect to pay out in compensation to bumped passengers?
c. Suppose you allow 220 reservations. What is the probability that you will have to deal with bumped passengers?