A workshop attended by a single mechanic has an average of five customers an hour who bring small appliances for repair. The mechanic inspects these for defects and often repairs them right away or renders a diagnosis. This takes him ten minutes, on the average. Arrivals are Poisson and service time has the exponential distribution. (a) Calculate the proportion of time during which the shop is empty. (b) Find the probability of determining at least one customer in the system. (c) Find the average number of customer in the system. (d) Determine the average time spent, including service.