customer arrival departure

$1.9$:$05$ AM$.9$:$26$ AM

$2.9$:$26$ AM$.9$:$44$ AM

$3.9$:$47$ AM$.10$:$12$ AM

$4.10$:$06$ AM$.10$:$23$ AM

$5.10$:$28$ AM$.10$:$43$ AM

$6.11$:$00$ AM$.11$:$32$ AM

$7.11$:$15$ AM$.11$:$33$ AM

$8.11$:$41$ AM$.12$:$04$ PM

$9.11$:$58$ AM$.12$:$21$ PM

$10.12$:$27$ PM$.1$:$00$ PM

$11.12$:$44$ PM$.1$:$15$ PM

$12.1$:$14$ PM$.1$:$36$ PM

$13.1$:$34$ PM$.1$:$55$ PM

$14.2$:$01$ PM$.2$:$24$ PM

$15.2$:$27$ PM$.2$:$46$ PM

$16.2$:$41$ PM$.3$:$10$ PM

$17.3$:$10$ PM$.3$:$37$ PM

$18.3$:$29$ PM$.3$:$49$ PM

$19.3$:$48$ PM$.4$:$03$ PM

$20.4$:$16$ PM$.4$:$46$ PM

$21.4$:$43$ PM$.5$:$12$ PM

Bob decided to open a computer repair business. He

wants to analyze his business so he collected the following data on a specific day. Can you help him by analyzing his dataset and evaluating his model by addressing each of the following tasks?

ANSWER THESE QUESTIONS

a$.[5$pt$]$ Plot the number of people in the system vs time.

b$.[10$pt$]$ Compute the coefficient of variation for the inter$-$arrival times and the service times.

c$.[5$pt$]$ Compute the utilization.

d$.[10$pt$]$ Compute the average wait time from the data, and compare it to the average wait time

prediction.

e$.[10$pt$]$ Find the average number of customers in the system using the data and using Little$$s

law.

f$.$ Assume each customer waits exactly $20$ minutes before deciding to leave the system, if Bob did not start repairing his computer. Bob thinks that if he is losing more than $3$ customers per day, then he should hire someone to assist him. Should Bob hire someone?