# Math Help - Poisson Approximation

1. ## Poisson Approximation

An airline knows from past experience that 95% of passengers who buy tickets will not miss a given flight. The planes for this flight have 100 seats and the airline decides to sell 105 tickets. Use a Poisson approximation to compute the probability that more than 100 people would show up for the flight. If the airline wants to make sure that this kind of over-booking does not happen for more than 5% of the flights, how many tickets should they sell?

I am not sure how to go about this problem. Any help would be appreciated.

2. Originally Posted by Shapeshift
An airline knows from past experience that 95% of passengers who buy tickets will not miss a given flight. The planes for this flight have 100 seats and the airline decides to sell 105 tickets. Use a Poisson approximation to compute the probability that more than 100 people would show up for the flight. If the airline wants to make sure that this kind of over-booking does not happen for more than 5% of the flights, how many tickets should they sell?

I am not sure how to go about this problem. Any help would be appreciated.
If X is the number of seats that will be required, then $\mu = 95$.

3. ok so I got my lambda to be 99.75. Then my i's are 101, 102, up to 105. And I computed the probabilities for each and summed them and got a probability of 0.1848, or 18.48%.