During the 3 PM to 5 PM time period, cars arrive at a bank's drive-through window at an average rate of 15 customers per hour. Assume that the time between arrivals follows the exponential distribution. What is the probability that a randomly selected customer will arrive between 2 and 6 minutes after the previous customer?

Question

Quizplus · Accepted Answer

The exponential distribution is given by the formula $P(X > x) = e^{-\lambda x}$, where $\lambda$ is the rate parameter (customers per minute in this case). Since there are 15 customers per hour, $\lambda = 15/60 = 0.25$ customers per minute. The probability that a customer arrives between 2 and 6 minutes is the difference between the probabilities that a customer arrives after 2 minutes and after 6 minutes. Thus, $P(2 < X < 6) = e^{-0.25*2} - e^{-0.25*6} = e^{-0.5} - e^{-1.5} \approx 0.3834$.

During the 3 PM to 5 PM Time Period, Cars