Answer Happy

Problem 5 (Binomial Distribution). Airlines regularly overbook flights to compensate for no-show passengers. In doing so, airlines are balancing the risk of having to compensate bumped passengers against lost revenue associated with empty seats. In a USA Today analysis of airline statistics, it was found that the average no-show rate was 12%. An airline books 110 passengers on a 100-seat plane. Assume a 12% probability that a passenger will not show up for boarding. (5.1) Easy. What is the probability that no passenger will be bumped? (5.2) Easy. What is the probability that the plane will be full? (5.3) Challenging. The airline makes a profit of $100 per passenger on this flight, and it estimates the cost of a bumped passenger to be $1000 (this includes cash awards to bumped passengers, free air vouchers, loss of goodwill, etc.). For this reason, the airline would like a probability of at least 0.9 that no passenger will be bumped. How many tickets should the airline sell on this 100-seat plane?