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, 10 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 five minutes each. Assume the queue length can be infinite with FCFS discipline.

c. What is the average amount of time that a person can expect to spend in line?

Short answer

Numerous financial and budgetary information show up as check factors, such as how multiple times an individual gets to be unemployed in a given year, hence loaning themselves to examination with a Poisson distribution.

Step-by-step solution

Step by step solution Step1: Poisson distribution is

In measurements, a Poisson distribution may be likelihood dissemination that's utilized to appear how numerous times an occasion is likely to occur over an indicated period. In other words, it could be a tally conveyance. Poisson conveyances are regularly utilized to get autonomous occurrences at a steady rate inside a given interim of time.

Average waiting time in the line is calculated as follows:

The average waiting time in the line is

$\begin{array}{l}{\text{W}}_{\text{q\hspace{0.17em}}}\text{\hspace{0.17em}=\hspace{0.17em}}\frac{{\text{L}}_{\text{q}}}{\text{λ}}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}=}\frac{\text{4.17}}{\text{10}}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}=\hspace{0.17em}0.417\hspace{0.17em}hour\hspace{0.17em}or\hspace{0.17em}25.02\hspace{0.17em}minutes}\end{array}$

Hence, the average amount of time that a person can expect to spend in line is

0.417 hours or 25.02 minutes.