Answered: Willow Brook National Bank operates a…

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

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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Question

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 48 customers per hour or 0.8 customers per minute. Assume the Poisson probability distribution can be used to describe the arrival process.

(a)

What is the mean or expected number of customers that will arrive in a five-minute period?

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 48 customers per hour or 0.8 customers per minute. Assume the Poisson
probability distribution can be used to describe the arrival process.
(a) What is the mean or expected number of customers that will arrive in a five-minute period?
(b) Use the arrival rate in part (a) and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a five-minute period. (Round your answers to
four decimal places.)
X
0
1
2
3
P(x)
(c) Delays are expected if more than three customers arrive during any five-minute period. What is the probability that delays will occur? (Round your answer to four
decimal places.)

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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