Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the proba

Question

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. n = 30, x = 12, p = 0.20

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Eliza 2 weeks 2021-09-10T06:49:36+00:00 1 Answer 0

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    2021-09-10T06:51:07+00:00

    Answer:

    P(X = 12) = 0.0064.

    Step-by-step explanation:

    Binomial probability distribution

    The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

    P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

    In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

    C_{n,x} = \frac{n!}{x!(n-x)!}

    And p is the probability of X happening.

    In this problem we have that:

    n = 30, p = 0.2

    We want P(X = 12). So

    P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

    P(X = 12) = C_{30,12}.(0.2)^{12}.(0.8)^{18} = 0.0064

    P(X = 12) = 0.0064.

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