In: Statistics and Probability
Suppose that the probability that a passenger will miss a flight is 0.0943. Airlines do not like flights with empty seats, but it is also not desirable to have overbooked flights because passengers must be "bumped" from the flight. Suppose that an airplane has a seating capacity of 58 passengers.
(a) If 60 tickets are sold, what is the probability that 59 or 60 passengers show up for the flight resulting in an overbooked flight?
(b) Suppose that 64 tickets are sold. What is the probability that a passenger will have to be "bumped"?
(c) For a plane with seating capacity of 53 passengers, how many tickets may be sold to keep the probability of a passenger being "bumped" below
55%?