In a recent​ year, a hospital had 4386 births. Find the mean number of births per​ day, then use that result and the Poisson distribution to

Question

In a recent​ year, a hospital had 4386 births. Find the mean number of births per​ day, then use that result and the Poisson distribution to find the probability that in a​ day, there are 14 births. Does it appear likely that on any given​ day, there will be exactly 14 ​births?

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Abigail 1 week 2021-09-11T04:33:12+00:00 1 Answer 0

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    2021-09-11T04:34:51+00:00

    Answer:

    9.08% probability that in a​ day, there are 14 births. So it does not appear likely that on any given​ day, there will be exactly 14 ​births.

    Step-by-step explanation:

    In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

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

    In which

    x is the number of sucesses

    e = 2.71828 is the Euler number

    \mu is the mean in the given time interval.

    In a recent​ year, a hospital had 4386 births.

    An year has 365 days. So \mu = \frac{4386}{365} = 12.02

    Find the probability that in a​ day, there are 14 births. Does it appear likely that on any given​ day, there will be exactly 14 ​births?

    This is P(X = 14).

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

    P(X = 14) = \frac{e^{-12.02}*(12.02)^{14}}{(14)!} = 0.0908

    9.08% probability that in a​ day, there are 14 births. So it does not appear likely that on any given​ day, there will be exactly 14 ​births.

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