7:591 · LTE . ezto.mheducation.com E connect Problem 7-18 To support National He

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7:591 · LTE . ezto.mheducation.com E connect Problem 7-18 To support National Heart Week, the Heart Association plans to install a free blood pressure testing booth in Con Mal for the week Previous experience ndcates hat, on average. 7.5 persons per hour request a test. Assume armas poisson distrbuted from, an infinite population Blood pressure measurer bende at a stant time of six minutes each. Assume the queue length can be infinite with FCFS discipline. a. What average number in line can be expecied? (Round your answer to 3 decimal places.) Average number expected people b, what average number of persons can be expected to be answer to 3 decimal places.) system?(Round your Average number of personspersons c. What is the average amount of time that a person can expect to spend in line7 (Round your answer to 4 decimal places Average an oundnne ]hours d. On the average, how much time will i take to measure a person's blood pressure including waiting time? (Round your answer to 4 decimal places Time takern

Explanation / Answer

Mean arrival rate ( Lambda) = 7.5 persons / hr

Mean service rate( Mu) = 60/6 = 10 persons /hr.

Utilization factor ( Rho)= Lambda / mu = 7.5/10 = 0.75

1. Avg number of persons waiting in the line = ( Rho)2 / 1-Rho = (0,75)2 / 1-0.75 = 2.25

2.Avg Number of persons to be in system = Rho / 1-Rho = 0.75/0.25 = 3

3. Avg time spent in queue = lambda / mu ( mu - lambda) = 7.5 / 10 ( 10-7.5) = 7.5 / 25 =0.3 hr = 18 min.

4. Avg time spent by a person = 1/ mu - lambda = 1/10-7.5 = 1/2.5 hr = 24 min.

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