Goliath Regional 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 teller window occur at random, with an arrival rate of 36 customers per hour. A drive-up teller can process an average of 50 customers per hour.
a) What is the mean or expected number of customers that will arrive in a 5-min period?
b) What is the service rate in terms of customers per 5-min period?
c) Assume that the Poisson distribution can be used to describe the arrival process. Use the arrival rate in part (a) and compute the probabilities that exactly 0, 1, and 2 customers will arrive during a 5-min period.
d) Delays are expected if more than 2 customers arrive during any 5-min period. What is the probability that delays will occur?
e) What is the probability that service time will be more than 2 minutes?