45 It can be shown that if events are occurring in time according to a Poisson distribution with mean λt, then the interarrival times between events have an 1 λ exponential distribution with mean Suppose that customers arrive at a checkout counter at the rate of two per minute. (a) What are the mean (in minutes) and variance of the waiting times between successive customer arrivals? min mean variance (b) If a clerk takes 2.7 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? (Round your answer to four decimal places.)

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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45
It can be shown that if events are occurring in time according to a Poisson distribution with mean λt, then the interarrival times between events have an
1
λ
exponential distribution with mean
Suppose that customers arrive at a checkout counter at the rate of two per minute.
(a) What are the mean (in minutes) and variance of the waiting times between successive customer arrivals?
min
mean
variance
(b) If a clerk takes 2.7 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? (Round your answer to four decimal places.)
Transcribed Image Text:45 It can be shown that if events are occurring in time according to a Poisson distribution with mean λt, then the interarrival times between events have an 1 λ exponential distribution with mean Suppose that customers arrive at a checkout counter at the rate of two per minute. (a) What are the mean (in minutes) and variance of the waiting times between successive customer arrivals? min mean variance (b) If a clerk takes 2.7 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? (Round your answer to four decimal places.)
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