Problem $1)(12$ points$)$ Che $7$

A call center has analyzed the calls received in the last month and found that, on average, $40$ calls were received per hour. Assume that call arrivals follow Poisson distribution and come from an infinite population. Service times follow an exponential distribution with an average of $75$ seconds per call served. Assume the queue length can be infinite with FCFS discipline.

a$)$ What is the average number of people in line? $(2\mathrm{.}5$ points$)$

b$)$ What is the average number of people in the system? $(2\mathrm{.}5$ points$)$

c$)$ What is the average amount of time that a person can expect to spend in line? $(2\mathrm{.}5$ points$)$

d$)$ On average, how much time will a person spend in the system? $(2\mathrm{.}5$ points$)$

e$)$ During the weekends, the call arrival rate can be expected to increase to over $40$ per hour. What effect will this have on the average number of people waiting in line? $(2$ points$)$