Customers checking out at Food Tiger arrive in a single-line queue served by two cashiers at a rate of 9 per hour according to a Poisson distribution. Each cashier processes customers at a rate of 7 per hour according to an exponential distribution. (a) If, on average, customers spend 31 minutes shopping before getting in the checkout line, what is the average time (in minutes) a customer spends in the store? (Round your answer to two decimal places.) ______ minutes (b) What is the average number of customers waiting for service in the checkout line? (Round your answer to four decimal places.) ______ customers (c) What is the probability that a customer must wait? (Round your answer to four decimal places.)
Customers checking out at Food Tiger arrive in a single-line queue served by two cashiers at a rate of 9 per hour according to a Poisson distribution. Each cashier processes customers at a rate of 7 per hour according to an exponential distribution. (a) If, on average, customers spend 31 minutes shopping before getting in the checkout line, what is the average time (in minutes) a customer spends in the store? (Round your answer to two decimal places.) ______ minutes (b) What is the average number of customers waiting for service in the checkout line? (Round your answer to four decimal places.) ______ customers (c) What is the probability that a customer must wait? (Round your answer to four decimal places.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
Customers checking out at Food Tiger arrive in a single-line queue served by two cashiers at a rate of 9 per hour according to a Poisson distribution. Each cashier processes customers at a rate of 7 per hour according to an exponential distribution.
(a) If, on average, customers spend 31 minutes shopping before getting in the checkout line, what is the average time (in minutes) a customer spends in the store? (Round your answer to two decimal places.)
______ minutes
(b) What is the average number of customers waiting for service in the checkout line? (Round your answer to four decimal places.)
______ customers
(c) What is the probability that a customer must wait? (Round your answer to four decimal places.)
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