The probability that a machine part is defective is 0.1. Find the probability that no more than 2 out of 12 parts tested are defective.

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The probability that a machine part is defective is 0.1. Find the probability that no more than 2 out of 12 parts tested are defective.

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Kaylee 2 months 2021-10-06T19:18:14+00:00 1 Answer 0 views 0

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    2021-10-06T19:20:09+00:00

    Answer:

    Probability that no more than 2 out of 12 parts tested are defective is 0.8891.

    Step-by-step explanation:

    We are given that the probability that a machine part is defective is 0.1.

    Twelve parts are selected at random.

    The above situation can be represented through binomial distribution;

    P(X = r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,.......

    where, n = number trials (samples) taken = 12 parts

                r = number of success = no more than 2

                p = probability of success which in our question is probability that

                      a machine part is defective, i.e; p = 0.1

    Let X = Number of machine parts that are defective

    So, X ~ Binom(n = 12, p = 0.1)

    Now, Probability that no more than 2 out of 12 parts tested are defective is given by = P(X \leq 2)

    P(X \leq 2) =  P(X = 0) + P(X = 1) + P(X = 2)

    = \binom{12}{0} \times 0.1^{0} \times (1-0.1)^{12-0}+\binom{12}{1} \times 0.1^{1} \times (1-0.1)^{12-1}+\binom{12}{2} \times 0.1^{2} \times (1-0.1)^{12-2}

    =   1\times 1 \times 0.9^{12}+ 12 \times 0.1^{1}  \times 0.9^{11}+ 66\times 0.1^{2}  \times 0.9^{10}

    =  0.8891

    Therefore, probability that no more than 2 out of 12 parts tested are defective is 0.8891.

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