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, with an arrival rate of 30 customers per hour or 0.5 customers per minute. Let's assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 45 customers per hour, or 0.75 customers per minute. Determine the following operating characteristics for the system. (Round your answers to four decimal places.) (a) The probability that no customers are in the system 1353 (b) The average number of customers waiting 1786 (c) The average number of customers in the system 1.25 x
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, with an arrival rate of 30 customers per hour or 0.5 customers per minute. Let's assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 45 customers per hour, or 0.75 customers per minute. Determine the following operating characteristics for the system. (Round your answers to four decimal places.) (a) The probability that no customers are in the system 1353 (b) The average number of customers waiting 1786 (c) The average number of customers in the system 1.25 x
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text: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, with an arrival rate of 30 customers per hour or 0.5 customers per minute.
Let's assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 45 customers per hour, or
0.75 customers per minute.
Determine the following operating characteristics for the system. (Round your answers to four decimal places.)
(a) The probability that no customers are in the system
1353
(b) The average number of customers waiting
1786
(c) The average number of customers in the system
1.25
(d) The average time (in min) a customer spends waiting
4.2
X min
(e) The average time (in min) a customer spends in the system
x min
1
(f) The probability that arriving customers will have to wait for service
73
X
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