Problem $3.(15$ points$)$ Colorado National Bank is considering opening a human$-$staffed, drive$-$

through window at one of its locations to enhance customer service. Management estimates

that customers desiring a human teller will arrive at the rate of $\frac{15}{?}$ hour. Based on historical

data, the tellers who will staff the window can service customers in an average time of $3$

minutes.

Assuming Poisson arrivals and exponential service times find:

a$)$ The utilization of the teller

b$)$ Average number in the waiting line

c$)$ Average number in the system

d$)$ Average waiting time in line

e$)$ Average waiting time in the system