People arrive to buy tickets at a movie theater according to a Poisson process with an average rate of 12 customers per hour. The time it takes to complete the sale of a ticket to each person is...

People arrive to buy tickets at a movie theater according to a Poisson process with an average rate of 12 customers per hour. The time it takes to complete the sale of a ticket to each person is exponentially distributed with a mean of 3 minutes. There is only one cashier at the ticket window, and any arriving customer that finds the cashier busy joins a queue that is served in an FCFS manner.

a. What is the probability that an arriving customer does not have to wait?

b. What is the mean number of waiting customers at the window?

c. What is the mean waiting time of an arbitrary customer?