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 14 persons per hour request test. Assume arrivals are Poisson distributed from an infinite population. Blood pressure measurements can be made at a constant time of four minutes each. Assume the queue length can be infinite with FCFS discipline.
a. What average number in line can be expected? Round answer to 2 decimal places.

Average number expected _____ people

b. What average number of persons can be expected to be in the system? Round answer to 4 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 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 answer to 4 decimal places.

Time taken _____ hours

Answer 1

Answer:

(a) Average number expected = 13.07 people

(b) Average number of persons = 14 persons

(c) Average amount of time = 0.9333 hours

(d) Time taken = 1 hour

Step-by-step explanation:

We are informed that the arrivals have a Poisson distribution from an infinite population. On average, 14 persons per hour request a test. Hence,

Arrival rate = λ = 14

Each blood pressure measurement takes 4 minutes. In 1 hour, 60 / 4 = 15 persons are served. Hence,

Service rate = μ = 15

(a) Average number in line = (λ^2) / μ(μ - λ)

                                             = (14^2) / 15(15 - 14)

                                             = 13.07

(b) Average number in system = λ / (μ - λ)

                                                   = 14 / (15 - 14)

                                                   = 14

(c) Average waiting time = Average number in line / λ

                                         = 13.07 / 14

                                         = 0.9333

(d) Average total time = Average number in system / λ

                                     = 14 / 14

                                     = 1