Question

To support National Heart Week, the Heart Association plans to install a free blood pressure testing booth in El Con Mall for the week. Previous experience indicates that, on average, 9.0 persons per hour request a test. Assume arrivals are Poisson distributed from an infinite population. Blood pressure measurements can be made at a constant time of six minutes each. Assume the queue length can be infinite with FCFS discipline.

a. What average number in line can be expected? (Round your answer to 3 decimal places.)

Average number expected              people

b. What average number of persons can be expected to be in the system? (Round your answer to 3 decimal places.)

Average number of persons             persons

c. What is the average amount of time that a person can expect to spend in line? (Round your answer to 4 decimal places.)

Average amount of time             hours

d. On the average, how much time will it take to measure a person's blood pressure, including waiting time? (Round your answer to 4 decimal places.)

Answer 1

Let , Arrival rate = persons per hour request a test. (average number of customers arriving per   unt of time )

       Survice rate = mean service rate (average number of customers that can be served per unit of time .  

So here given Blood pressure measurements can be made at a constant time of six minutes each.

Mean survercice rate = 60/6 =10 , that is avrrage number of customers served per hours.

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a )What average number in line can be expected?

   

Average number expected     8.100 (8) people.

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What average number of persons can be expected to be in the system? (Round your answer to 3 decimal places.)

Average number in system= arrival rate/ (service rate –arrival rate)

Average number of persons 9.000 persons.

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What is the average amount of time that a person can expect to spend in line? (Round your answer to 4 decimal places.)

Average time waiting in line = average number waiting in line/arrival rate

Average amount of time 0.9 hours.

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On the average, how much time will it take to measure a person's blood pressure, including waiting time? (Round your answer to 4 decimal places.)

Average total time in the system = Average number in system/arrival rate