During late-night hours, the 10^th Street convenience store averages four customers per hour.No customers have arrived in the last half-hour.Assuming that all Poisson conditions are met, determine the probability that the next customer won't arrive for at least 45 more minutes. A).0498 B).0732 C).1430 D).4168 E).0992

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Quizplus · Accepted Answer

The average rate is 4 customers per hour, so 2 customers per half-hour. The probability of no customers arriving in 1.25 hours (2.5 half-hours) is given by the Poisson distribution: P(X=0) = e^(-2.5) * (2.5^0) / 0! = e^(-2.5) ≈ 0.0821. However, since no customers have arrived in the first half-hour, we need the probability for the next 45 minutes (1.5 half-hours), which is e^(-2) ≈ 0.1353. The probability that no customer arrives for at least 45 more minutes is e^(-2.5) / e^(-2) = e^(-0.5) ≈ 0.0498.

During Late-Night Hours, the 10th Street Convenience Store Averages Four

During Late-Night Hours, the 10^th Street Convenience Store Averages Four