A teller works at a rural bank. Customers arrive to complete their banking transactions on average one every 10 minutes; their arrivals follow a Poisson arrival process. Because of the range of possible transactions, the time taken to serve each customer may be as-sumed to follow an exponential distribution with a mean time of 7 minutes. Customers wait in a single queue to get their banking done, and no customer leaves without service.

Please specify your calculation process with an answer (If you do not specify, only 0.5 pts)

Calculate the average utilization of the teller.

Calculate how long customers spend on average to complete their transactions at the bank (hint: Consider "W-the expected time in the system").

How many customers are in the bank on average? (Hint: Little's formula)