A repair shop has space to accommodate only 5 customers in the system. The shop attended by a single mechanic has an average of 4 customers an hour who bring small appliances for repair. The mechanic inspects them for defects and quite often can fix them right away or otherwise render a diagnosis. This takes him 6 minutes, on the average. Arrivals are Poisson and service times are exponentially distributed random variables. Find the (i) Average time spent in the queue. (ii) The average queue length of a non-empty queue (iii) Proportion of time during which the shop is empty (iv) Probability of finding at least 1 customer in the shop (v) Average number of customers in the system