To support National Heart Week, the Heart Association plans to install a free blood pressure testing booth in El Con Mall for th

Question

2 years ago

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To support National Heart Week, the Heart Association plans to install a free blood pressure testing booth in El Con Mall for th

e 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

Mathematics

1 answer:

worty [1.4K] · Answer 1 · 2022-07-19T11:57:08+03:00

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