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Math Help - Probability - Poisson

  1. #1
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    Probability - Poisson

    Suppose that the number of chocolate chips in a cookie follows the poisson random variable with lambda=4.

    What is the probability that a package of 9 cookies will have exactly 36 chips?

    So I know that lambda is the mean so each cookie should have 4 chips on it which seems to correspond with the factg that 36/9 = 4 also.

    Does the mean change when you have more cookies?

    How would you set this problem up. I assume it will have something to do with:
    Pr = e^(neg lambda) * (lambda^y)/(y!)

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by DINOCALC09 View Post
    Suppose that the number of chocolate chips in a cookie follows the poisson random variable with lambda=4.

    What is the probability that a package of 9 cookies will have exactly 36 chips?

    So I know that lambda is the mean so each cookie should have 4 chips on it which seems to correspond with the factg that 36/9 = 4 also.

    Does the mean change when you have more cookies?

    How would you set this problem up. I assume it will have something to do with:
    Pr = e^(neg lambda) * (lambda^y)/(y!)

    Thanks in advance.
    Let X be the random variable "number of chips in packet of 9 cookies". Use Poisson with mean = (4)(9) = 36 and calculate Pr(X = 36).
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    Pr(X=36) = e^(-36) * [(36^36)/(36!)] = approx 0.0663 ???
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  4. #4
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    Since new lambda = 36 as a result of multiplying 4*9, that would mean a poisson model is probably not the best approximation since nm > 5, correct? Or am i misunderstanding something.
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