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12 April, 21:24

There is only one checkout line and the average service time is 5 minutes per customer. There are 3 people in the queue ahead of you. What is the probability that your wait time will exceed 7 minutes?

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Answers (2)
  1. 12 April, 22:46
    0
    The probability is 100% because 3*5 is 15, since 5 is the average time and 3 customers are already there.
  2. 12 April, 23:45
    0
    62.7%

    Step-by-step explanation:

    This is an example of a Poisson process:

    Events are independent The average rate is constant Events cannot happen simultaneously

    Using a Poisson distribution, the probability that the wait time T will exceed a certain time t is:

    P (T > t) = e^ (-events/time * t)

    The average wait time per customer is 5 minutes, so the expected wait time for 3 customers is 15 minutes.

    Given that t = 7 min and event/time = 1 / 15 min:

    P (T > 7) = e^ (-1/15 * 7)

    P (T > 7) = 0.627

    There is a 62.7% probability that your wait time will exceed 7 minutes.
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