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 87 seconds completing his or her transactions. Transaction time is exponentially distributed. Determine the following: a. The average time customers spend at the machine, including waiting in line and completing transactions b. The probability that a customer will not have to wait upon arriving at the automatic teller machine c. The average number waiting to use the machine
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 87 seconds completing his or her transactions. Transaction time is
exponentially distributed. Determine the following:
a. The average time customers spend at the machine, including waiting in line and completing
transactions
b. The probability that a customer will not have to wait upon arriving at the automatic teller
machine
c. The average number waiting to use the machine
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