# Airline Problem with Poisson Approximation

1. Oct 7, 2007

### mutzy188

1. The problem statement, all variables and given/known data

An ailrine always overbooks if possible. A particular plane ha 95 seats on a flight in which a ticket sells for $300. The airline sells 100 such tickets for this flight. Use a Poisson approximation only. (a) If the probbility of an individual not showing is 0.05, assuming independence, what is the probability that the airline can accomidate all the passengers who do show up? (b) If the airline must return the$300 price plus a penalty of $400 to each passenger that cannot get on the flight, what is the expected payout (penalty plus ticket refund) that the airline will pay? Answer =$598.56

3. The attempt at a solution

I know how to do part (a), and I got 0.560 as my answer, which agrees with the answer in the back of the book. I just don't know how to do part b.

My thoughts:

The probability that they cannot accomidate the passengers = 1 - .56 = 0.44.

3. Oct 7, 2007

### mutzy188

How do I find the expected number of passengers that will not show up?

4. Oct 7, 2007

6. Oct 8, 2007