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Suppose that customers arrive at a checkout counter at a
Chapter 4, Problem 171SE(choose chapter or problem)
Problem 171SE
Suppose that customers arrive at a checkout counter at a rate of two per minute.
a What are the mean and variance of thewaiting times between successive customer arrivals?
b If a clerk takes three minutes to serve the first customer arriving at the counter, what is the probability that at least one more customer will be waiting when the service to the first customer is completed?
Questions & Answers
QUESTION:
Problem 171SE
Suppose that customers arrive at a checkout counter at a rate of two per minute.
a What are the mean and variance of thewaiting times between successive customer arrivals?
b If a clerk takes three minutes to serve the first customer arriving at the counter, what is the probability that at least one more customer will be waiting when the service to the first customer is completed?
ANSWER:
Solution:
Step 1 of 2:
Suppose that customers arrive at a checkout counter at a rate of two per minute.
a). To find the mean and variance of the waiting times between successive customer arrivals.
Given
The mean of exponential distribution is
Then the variance is
=
Therefore, the mean and variance of the waiting times between successive customer arrivals is