Question 4

Customers at a bank wait in a single line for the next available teller. Customer arrivals can be modeled by a Poisson distribution that has an average of 6 per hour. A teller can process an average of 10 customers per hour, which also can be modeled by a Poison distribution (that is to say that the service time is exponentially distributed). If there is one teller on duty, determine:

(a) The average time a customer must wait in line.

(b) The average number of customers waiting in line.

(c) Average service time a customer takes.

(d) The probability that a customer will have to wait for service.

(e) The probability of no customers waiting in line.