A book has 200 pages. The number of mistakes on each page is a Poisson random variable with mean 0.01, and is independent of the number of m

Question

A book has 200 pages. The number of mistakes on each page is a Poisson random variable with mean 0.01, and is independent of the number of mistakes on all other pages. a. What is the expected number of pages with no mistakes

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Gabriella 3 weeks 2021-10-01T18:30:25+00:00 1 Answer 0

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    2021-10-01T18:32:11+00:00

    Answer:

    198 pages have no mistakes.                                      

    Step-by-step explanation:

    We are given the following in the question:

    The number of mistakes on a page follows a poison distribution with

    \mu = \lambda = 0.01

    Formula:

    P(X =k) = \displaystyle\frac{\lambda^k e^{-\lambda}}{k!}\\\\ \lambda \text{ is the mean of the distribution}

    We have to find the probability that there are no mistakes on a page.

    P(X =0) = \displaystyle\frac{(0.01)a^0 e^{-0.01}}{0!} = 0.9901

    Thus, approximately 99.01% of the pages have no mistakes.

    Number of pages =

    \text{Total number of pages}\times 99.01\%\\\\200\times \dfrac{99.01}{100}\\\\\approx 198

    Thus, 198 pages have no mistakes.

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