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 83 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 minutes 4 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
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 83 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 minutes 4 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
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter7: Integration
Section7.CR: Chapter 7 Review
Problem 88CR
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Transcribed Image Text: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 83 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
minutes
4
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
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