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Math Help - Problem using poisson Approximation

  1. #1
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    Problem using poisson Approximation

    If the probability that an individual suffers from bad reaction from an injection of a given serum is 0.001, determine the probability that out of 2000 individuals

    i) exactly 3 individuals will suffer a bad reaction
    ii) more than 2 individuals will suffer a bad reaction
    by using Poisson Approximation

    Also give exact probability (you need not simplify the expression)
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  2. #2
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    Quote Originally Posted by Stats View Post
    If the probability that an individual suffers from bad reaction from an injection of a given serum is 0.001, determine the probability that out of 2000 individuals

    i) exactly 3 individuals will suffer a bad reaction
    ii) more than 2 individuals will suffer a bad reaction
    by using Poisson Approximation

    Also give exact probability (you need not simplify the expression)
    Poisson approximation: The mean is \lambda = (0.001)(2000) = 2. Substitute this into the pmf of the Poisson distribution and use the pmf to do the calculations.

    What do you think the exact distribution is?

    For (ii) note that \Pr(X > 2) = 1 - \Pr(X \leq 2).
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