1. American Airlines Flight 179 from NewYork to San Francisco uses a Boeing 767-

Question

1.     American Airlines Flight 179 from NewYork to San Francisco uses a Boeing 767-300 with 213 seats. Becausesome people with reservations don’t show up, AmericanAirlines can overbook by accepting more than 213 reservations. Ifthe flight is not overbooked, the airline will lose revenue due toempty seats, but if too many seats are sold and some passengers aredenied seats, the airline loses money from the compensation thatmust be given to the bumped passengers. Assume that there is a0.0995 probability that a passenger with a reservation will notshow up for the flight (based on data from the IBM research paper“Passenger-Based Predictive Modeling of Airline No-ShowRates” by Lawrence, Hong, and Cherrier). Also, assume thatthe airline accepts 236 reservations for the 213 seats that areavailable.

a.     Find the probability that when 236reservations are accepted for Flight 179, there are more passengersshowing up than there are seats available. That is, find theprobability of more than 213 people showing up with reservations,assuming that 236 reservations were accepted. Round your answer tothree decimal places.

Explanation / Answer

While this can be constructed a binomial problem, the large numbersimply that a normal approximation can be used. The probability ofsuccess (person not showing up) is 0.0995, so the expected numberof people not showing up is 236*0.0995 = 23.482, with a variance of236*0.0995*(1-0.0995) = 21.1455 P(X > 23) = 1 - P(X

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