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Math Help - Problem with Poisson

  1. #1
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    Problem with Poisson

    I need help with this:

    "The number of defects in a certain plastic film follows a Poisson distribution with an average of 0.05 defects per square meter. To build a boat, an area of 3 m x 2 m must be covered with that film. In building 5 boats, what's the probability that at least 4 of them do not present defects in the plastic surface?"


    My reasoning: to build one boat, the total area is 6 m^2, so the number of defects is expected to be 0.05 * 6 = 0.3. For 5 boats, 0.3 * 5 = 1.5. If I use this value as lambda and calculate 1 - P(0) - P(1) I get 0.4422, which is wrong.

    The correct answer is 0.6135
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  2. #2
    MHF Contributor harish21's Avatar
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    at least 4 means: 4 or greater...

    P(X \geq 4) = P(X=4)+P(X=5)
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  3. #3
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    Quote Originally Posted by nvwxgn View Post
    I need help with this:

    "The number of defects in a certain plastic film follows a Poisson distribution with an average of 0.05 defects per square meter. To build a boat, an area of 3 m x 2 m must be covered with that film. In building 5 boats, what's the probability that at least 4 of them do not present defects in the plastic surface?"


    My reasoning: to build one boat, the total area is 6 m^2, so the number of defects is expected to be 0.05 * 6 = 0.3. For 5 boats, 0.3 * 5 = 1.5. If I use this value as lambda and calculate 1 - P(0) - P(1) I get 0.4422, which is wrong.

    The correct answer is 0.6135
    Let X be the random variable "Number of defects in a boat". Calculate p = Pr(X = 0).

    Let Y be the random variable "Number of boats with no defect". Then Y ~ Binomial(n = 5, p = above value). Calculate \Pr(Y \geq 4) = \Pr(Y = 4) + \Pr(Y = 5).
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