United Flight 15 from New York’s JFK airport to SanFrancisco uses a Boeing XXXXXXXXXXwith 182 seats. Because some people withreservations don’t show up, United can overbooked by accepting more than...

United Flight 15 from New York’s JFK airport to San Francisco uses a Boeing 757-200 with 182 seats. Because some people with reservations don’t show up, United can overbooked by accepting more than 182 reservations. If the flight is not overbooked, the airline will lose revenue due to empty seats, but if too many seats are sold and some passengers are denied seats, the airline loses money from the compensation that must be given to the bumped passengers. Assume that there is a 0.0995 probability that a passenger with a reservation will not show up for the flight (based on data from the IBM research paper “Passenger-Based Predictive Modeling of Airline No-Show Rates,” by Lawrence, Hong, and Cherrier). Also assume that the Airline accepts 200 reservations for the 182 seats that are available.

Find the probability that when 200 reservations are accepted for United Flight 15, there are more passengers showing up than there are seats that are available. Is the probability of overbooking small enough so that it does not happen very often, or does it seem too high so that changes must be made to make it lower? Now use trial and error to find the maximum number of reservations that could be accepted so that the probability of having more passengers than seats is 0.05 or less.