A particular flight from Chicago to Orlando has 224 seats Si

A particular flight from Chicago to Orlando has 224 seats. Since it is well documented that not all passengers show up for their seat reservation, the airline overbooks the flight by accepting more than 224 reservations. If the flight is not overbooked, the airline loses money due to open seats, but if too many seats are sold and some passengers are denied seats, then the airline loses money for the compensation it must give to those passengers.

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 available.

The mean is 21.9275. The standard deviation is 4.4682

Using this data, what is the \'usual\' range of passengers that you would not expect to show up? Would it be unusual for 25 people with reservations to NOT show up for the flight?

Solution

Probability that a passenger with a reservation will show up = 1 - 0.0895 = 0.9105

Total no.of passengers who will show up = 245 * 0.9105 = 223.07

Since , 223.07<224

The probability that more than 224 people with reservations actually show up for the flight = 0 Answer

The probability of overbooking small so that it does not appear very often.