Assume that at a bank teller window the customers arrive in their cars at the average rate of twenty per hour according to a Poisson distribution. Assume also that the bank teller spends an average of two minutes per customer to complete a service, and the service time is exponentially distributed. Customers, who arrive from an infinite population, are served on a first-come-first-served basis, and there is no limit to possible queue length.

(i) What is the expected waiting time in the system per customer?

(ii) What is the mean number of customers waiting in the system?

(iii) What is the probability of zero customers in the system?

(iv) What value is the utilisation factor?