30 points Save Ansy Customers arrive in a barber shop at an average re of five per hour, the actual arrivals being Poisson distributed. There is one barber on duty at all times and there are four chairs for customers who arrive when the barber is busy. Local fire ordinances limit the total number of customers in the shop at the same time to maximum of five. Customers who arrive when the shop is full are denied entrance and their business is presumed lost. The barber's service time is exponentially distributed, but the mean changes with the number of customers in the shop. As the shop fills, the barber tries to speed service, but actually becomes less efficient, as shown in the following table: Number in Shop 2 3 4 5 Mean Service 9 10 12 15 20 Time, minute Determine: a) the probability that the barber is idle. Answer in 4 decimal places. b) the average number of people in the shop at the same time. Answer in 3 decimal places