4) (2 pts) A certain small grocery store has a single checkout stand with a full-time cashier. Customers arrive at the stand "randomly" (i.e., a Poisson input process) at a mean rate of 30 per hour. When there is only one customer at the stand, she is processed by the cashier alone, with an expected service time of 1.5 minutes. However, the stock boy has been given standard instructions that whenever there is more than one customer at the stand, he is to help the cashier by bagging the groceries. This help reduces the expected time required to process a customer to 1 minute. In both cases, the service-time distribution is exponential. a) Derive the analytical steady-state probability distribution for the number of customers at the checkout stand. b) How much average customer wait time is saved under this policy compared to a M/M/1 policy? (hint: n=0nxn=(1x)2x )