The amount of time it takes Emma to wait for the train is continuous and uniformly distributed between 4 minutes and 11 minutes. What is the

Question

The amount of time it takes Emma to wait for the train is continuous and uniformly distributed between 4 minutes and 11 minutes. What is the probability that it takes Emma more than 5 minutes to wait for the train?

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Claire 3 weeks 2021-09-26T18:58:12+00:00 1 Answer 0

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    2021-09-26T18:59:50+00:00

    Answer:

    85.71% probability that it takes Emma more than 5 minutes to wait for the train

    Step-by-step explanation:

    An uniform probability is a case of probability in which each outcome is equally as likely.

    For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

    The probability that we find a value X lower than x is given by the following formula.

    P(X \leq x) = \frac{x - a}{b-a}

    Uniformly distributed between 4 minutes and 11 minutes.

    This means that a = 4, b = 11.

    What is the probability that it takes Emma more than 5 minutes to wait for the train?

    Either it takes 5 or less minutes, or it takes more than 5 minutes. The sum of the probabilities of these events is 1. So

    P(X \leq 5) + P(X > 5) = 1

    We want to find P(X > 5). So

    P(X > 5) = 1 - P(X \leq 5) = 1 - \frac{5 - 4}{11 - 4} = 0.8571

    85.71% probability that it takes Emma more than 5 minutes to wait for the train

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