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Math Help - Poisson Approximation

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by Shapeshift View Post
    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.
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  3. #3
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    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%.
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