Your grocery store has a single payment counter. On average the customer has 12 items. The cashier can process a customer with 12 items in 3 minutes, according to a negative exponential distribution. Customers wanting to pay arrive at the checkout line on the average of 15 per hour, following a Poisson distribution. The customer is served on a first-in, first-out basis and come from a very large (almost infinite) population of possible buyers. Determine a) Average number of units (customers in the system (waiting and being served) (3 marks) b) Average time a unit spends waiting in the queue (4 marks). c) Probability of 0 units in the system