Records show that the average number of phone calls received per day is 9.2. Find the probability of between 2 and 4 phone calls received (e

Question

Records show that the average number of phone calls received per day is 9.2. Find the probability of between 2 and 4 phone calls received (endpoints included) in a given day.

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Maria 1 month 2021-10-18T14:33:51+00:00 1 Answer 0 views 0

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    2021-10-18T14:34:58+00:00

    Answer:

    4.76% probability of between 2 and 4 phone calls received (endpoints included) in a given day.

    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 interval.

    Records show that the average number of phone calls received per day is 9.2.

    This means that \mu = 9.2.

    Find the probability of between 2 and 4 phone calls received (endpoints included) in a given day.

    (2 \leq X \leq 4) = P(X = 2) + P(X = 3) + P(X = 4)

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

    P(X = 2) = \frac{e^{-9.2}*(9.2)^{2}}{(2)!} = 0.0043

    P(X = 3) = \frac{e^{-9.2}*(9.2)^{3}}{(3)!} = 0.0131

    P(X = 4) = \frac{e^{-9.2}*(9.2)^{4}}{(4)!} = 0.0302

    (2 \leq X \leq 4) = P(X = 2) + P(X = 3) + P(X = 4) = 0.0043 + 0.0131 + 0.0302 = 0.0476

    4.76% probability of between 2 and 4 phone calls received (endpoints included) in a given day.

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45:7+7-4:2-5:5*4+35:2 =? ( )