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Math Help - Poisson distribution

  1. #1
    Junior Member
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    Poisson distribution

    Hi

    I need help setting this up.

    Grasshoppers are distributed at random in a large field according to a Poisson distribution with parameter alpha = 2 per square yard. How large should the radius R of a circular sampling region be taken so that the probability of finding at least one in the region equals .99?

    I think the problem I'm having is with the square yard and radius. I know that to calculate pr(x =>1) = 1 - pr(x = 0).
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by shogunhd View Post
    Hi

    I need help setting this up.

    Grasshoppers are distributed at random in a large field according to a Poisson distribution with parameter alpha = 2 per square yard. How large should the radius R of a circular sampling region be taken so that the probability of finding at least one in the region equals .99?

    I think the problem I'm having is with the square yard and radius. I know that to calculate pr(x =>1) = 1 - pr(x = 0).
    Let the radius of the sampling region be r yards, then the area of the sampling region is \pi r^2, and the mean number of grasshoppers in the sampling region is 2 \pi r^2.

    RonL
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