In San Francisco, 30% of workers take public transportation daily. In a sample of 10 workers, what is the probability that exactly three wor

Question

In San Francisco, 30% of workers take public transportation daily. In a sample of 10 workers, what is the probability that exactly three workers take public transportation daily?

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Katherine 3 months 2021-10-19T22:12:37+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-19T22:14:33+00:00

    Answer:

    26.68% probability that exactly three workers take public transportation daily

    Step-by-step explanation:

    For each worker, there are only two possible outcomes. Either they take public transportation daily, or they do not. The probability of a worker taking public transportation daily is independent from other workers. So we use the binomial probability distribution to solve this question.

    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.

    30% of workers take public transportation daily.

    This means that p = 0.3

    In a sample of 10 workers, what is the probability that exactly three workers take public transportation daily?

    This is P(X = 3) when n = 10. So

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

    P(X = 3) = C_{10,3}.(0.3)^{3}.(0.7)^{7} = 0.2668

    26.68% probability that exactly three workers take public transportation daily

    0
    2021-10-19T22:14:34+00:00

    Answer:

    0.267

    Step-by-step explanation:

    p = 0.3 q = 0.7

    10C3 × p³ × q⁷

    0.266827932

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