A particular United Airlines flight from Chicago to Orlando has 224 seats. Since

Question

A particular United Airlines flight from Chicago to Orlando has 224 seats. Since it is well documented that not all passengers show up for their seat reservation, United routinely overbooks the flight by accepting more than 224 reservations. If the flight is not overbooked, the airline loses money due to empty seats, but if too many seats are sold and some passengers denied seats, then the airline loses money from the compensation it must give to the bumped passengers (usually in the form of a ticket voucher for a future flight). Assume that there is a .0895 probability that a passenger with a reservation on this flight will not show up. Also assume that the airline accepts 245 reservations for the 224 seats that are available. 1. First, in terms of passengers showing up for their reservations,describe how this specific problem represents a Binomial Probability problem. Do this by using all the requirements of a Binomial Probability distribution and describing how this problem fits each requirement.

Explanation / Answer

From the given information number of trials are fixed(224) and the probability succes is known(0.0895). So, apply binomial distribution.

The mean is np=245*0.0895=22

The standard deviation is np(1-p)=245*0.0895(1-0.0895)=4.5

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