3. Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of seven per hour. a. During a given hour, what is the probability that no more than three customers arrive? b. During a given hour, what is the probability that at least two customers arrive? c. During a given hour, what is the probability that exactly five customers arrive?
3. Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of seven per hour. a. During a given hour, what is the probability that no more than three customers arrive? b. During a given hour, what is the probability that at least two customers arrive? c. During a given hour, what is the probability that exactly five customers arrive?
A First Course in Probability (10th Edition)
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![3. Customers arrive at a checkout counter in a department store according to a Poisson
distribution at an average of seven per hour.
a. During a given hour, what is the probability that no more than three customers arrive?
b. During a given hour, what is the probability that at least two customers arrive?
c. During a given hour, what is the probability that exactly five customers arrive?
f. What is the probability that exactly two customers arrive in the two-hour period of
time between a 2:00 P.M. and 4:00 P.M. (one continuous two-hour period)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd48b8819-fa93-4be0-8e21-0a11df5ef5a7%2Fa491208c-f18b-41d9-8728-6f59f0391869%2Femepj7s.jpeg&w=3840&q=75)
Transcribed Image Text:3. Customers arrive at a checkout counter in a department store according to a Poisson
distribution at an average of seven per hour.
a. During a given hour, what is the probability that no more than three customers arrive?
b. During a given hour, what is the probability that at least two customers arrive?
c. During a given hour, what is the probability that exactly five customers arrive?
f. What is the probability that exactly two customers arrive in the two-hour period of
time between a 2:00 P.M. and 4:00 P.M. (one continuous two-hour period)?
![d. If it takes approximately ten minutes to serve each customer, find the mean and vari-
ance of the total service time for customers arriving during a 1-hour period.
e. Using part [d.], is it likely that the total service time will exceed 2.5 hours?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd48b8819-fa93-4be0-8e21-0a11df5ef5a7%2Fa491208c-f18b-41d9-8728-6f59f0391869%2Fkkf8cpg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:d. If it takes approximately ten minutes to serve each customer, find the mean and vari-
ance of the total service time for customers arriving during a 1-hour period.
e. Using part [d.], is it likely that the total service time will exceed 2.5 hours?
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