To maximize the efficiency at a coffee shop, the manager has decided to adopt an automatic coffee serving machine. It can do all the tasks including taking orders, making coffees, and serving customers. Previous experience indicates that, on the average, 15 persons per hour comes to the coffee shop. Assume arrivals are Poisson distributed from an infinite population. The machine can serve each customer at a constant time of three minutes for any orders. Assume the queue length can be infinite with FCFS discipline.

a. What is the average number of people in the waiting line expected? (Enter only a number with one decimal place., e.g. 1.2 people --> 1.2)

b. On the average, how much time will it take for a customer to get out the shop with a coffee, including waiting time? (Enter a number in minutes with one decimal place., e.g., 12.3 minutes --> 12.3)

c. What would be the average time for customer to spend at the coffee shop (from entering to exiting) if the manager switches back to human servers instead of the machine? Assume that the human servers can serve at the same rate (i.e., 3 minutes per customer), but the serving time follows exponential distribution. (Enter a number in minutes with one decimal place., e.g., 12.3 minutes --> 12.3)