# Means & Poisson Distributions

A bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up window occur at random, with a mean arrival rate of 24 customers per hour or 0.4 customers per minute.

1) What is the mean or expected number of customers that will arrive in a five minute period?

2) Assume that the Poisson probability distribution can be used to describe the arrival process. Use the mean arrival rate in part 1 and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a five-minute period.

3) Delays are expected if more than three customers arrive during any five-minute period. What is the probability that delays will occur?

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#### Solution Summary

Simple calculations needed to work out the expected number of customers at a drive-thru, as well as how many will arrive in a five-minute period assuming a Poisson distribution, are attached in Word.