In: Statistics and Probability
Many of a bank’s customers use its automatic teller machine to transact business after normal banking hours. During the early evening hours in the summer months, customers arrive at a certain location at the rate of one every other minute. This can be modeled using a Poisson distribution. Each customer spends an average of 99 seconds completing his or her transactions. Transaction time is exponentially distributed.
a. Determine the average time customers spend at
the machine, including waiting in line and completing transactions.
(Do not round intermediate calculations. Round your answer
to the nearest whole number.)
Average time in minutes
b. Determine the probability that a customer will
not have to wait upon arriving at the automatic teller machine.
(Round your answer to 2 decimal places.)
Probability
c. Determine the average number of customers
waiting to use the machine. (Round your answer to 2 decimal
places.)
Average number of customers