2. Willow Brook National 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. Assume that Poisson probability distribution with an arrival rate of 24 customers per hour or 0.4 customer per minute can be used to describe the arrival pattern. Assume further that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour, or 0.6 customer per minute. Use the single-channel drive-up bank teller operation to determine the following operating characteristics for the system:
2. Willow Brook National 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. Assume that Poisson probability distribution with an arrival rate of 24 customers per hour or 0.4 customer per minute can be used to describe the arrival pattern. Assume further that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour, or 0.6 customer per minute. Use the single-channel drive-up bank teller operation to determine the following operating characteristics for the system:
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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Transcribed Image Text:2. Willow Brook National 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. Assume
that Poisson probability distribution with an arrival rate of 24 customers per hour or 0.4
customer per minute can be used to describe the arrival pattern. Assume further that
the service times for the drive-up teller follow an exponential probability distribution
with a service rate of 36 customers per hour, or 0.6 customer per minute. Use the
single-channel drive-up bank teller operation to determine the following operating
characteristics for the system:
a. The probability that no customers are in the system
b. The average number of customers waiting
c. The average number of customers in the system
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