A restaurant gets an average of 5.3 complaints per day from its patrons. Use the Poisson distribution formula to find the probability that o

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A restaurant gets an average of 5.3 complaints per day from its patrons. Use the Poisson distribution formula to find the probability that on a given day the restaurant will receive

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Adela 3 years 2021-08-16T09:53:08+00:00 1 Answers 0 views 0

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  1. ThanhThu
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    2021-08-16T09:54:21+00:00
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    Question: A restaurant gets an average of 5.3 complaints per day from its patrons. Use the Poisson distribution formula to find the probability that on a given day the restaurant will receive  exactly 4 complaints

    Answer:

    P(X=4) = 0.164125

    Step-by-step explanation:

    Given

    \bar{x} = 5.3 — average

    Required

    Determine the probability of receiving 4 complaints in a day

    Since, it follows a poisson distribution, the probability is calculated as:

    P(X=x) = \frac{\bar{x}^x * e^{-\bar{x}}}{x!}

    In this case:

    x = 4

    So, we have:

    P(X=4) = \frac{5.3^4 * e^{-5.3}}{4!}

    P(X=4) = \frac{789.0481 * 0.004992}{4*3*2*1}

    P(X=4) = \frac{3.939}{24}

    P(X=4) = 0.164125

    Hence, the probability of exactly 4 complaints is 0.164125
    .

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