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 standard deviation for this probability distribution?

Question

Quizplus · Accepted Answer

The standard deviation for an exponential distribution is the inverse of the rate (λ), which in this case is 15 customers per hour or 1/15 of an hour per customer. Converting hours to minutes gives us 60/15 = 4 minutes. However, the correct calculation for the standard deviation in this context is actually the inverse of the rate without needing to convert into minutes, leading to a misunderstanding in the explanation. The correct interpretation should be that for an exponential distribution, the standard deviation is the inverse of the rate, λ, which when dealing with time between arrivals, directly translates to the same value as the mean. Since the arrivals are 15 customers per hour, the mean time between arrivals is 1/15 hours. To find the standard deviation in minutes, we convert this to minutes: (1/15) * 60 = 4 minutes, making the correct answer 4 minutes, not 2 minutes as previously stated.

During the 3 PM to 5 PM Time Period, Cars