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Probability Poisson

  1. Oct 29, 2013 #1
    1. The problem statement, all variables and given/known data

    Suppose that 1% of cars have defective brake lights and n cars are to be inspected. How large should n be for the sample to have a probability of at least 50% of containing a car with a defective brake light? Give an answer using a Poisson approximation with an appropriate mean.

    3. The attempt at a solution

    Let X-Bin(n, 0.01).
    We can approximate X with the Poisson distribution assuming n large and with mean 0.01n.
    That is, X≈Po(0.01n).
    We want P(X=1)≥ 0.5 which yields ne^-0.01n ≥ 50.

    Then I'm stuck. Is this correct so far and any direction on where to go from here will be appreciated. Thanks.
     
  2. jcsd
  3. Oct 29, 2013 #2

    pasmith

    User Avatar
    Homework Helper

    I think you actually want [itex]P(X \geq 1) \geq 0.5[/itex], since a sample which contains more than one defective car contains a defective car.
     
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