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Problem 2: You normally receive primary healthcare from a small local clinic. The clinic has three doctors, Dr. Phyllis Nelson, Dr. Diane Hollman, and Dr. David Young. The clinic is open 24 hours a day. At any time, only one of the physicians is on duty. Dr. Nelson works from 8 am to 4 pm; Dr. Hollman works from 4 pm to midnight; and Dr. Young (naturally the youngest of the three physicians) works from midnight until 8 am. The clinic operates 7 days a week. Patients generally arrive at the clinic at a rate of 3 per hour according to a Poisson process. The physicians spend an average of 15 minutes with each patient and the service times are exponentially distributed. a) What is the service rate (in patients per hour)? b) What is the average number of patients in the system? C) What is the average time a patient spends in the system? Give your answer in hours. d) What is the average time a patient spends waiting to see one of the doctors? Again, give your answer in hours. e) What is the average number of patients waiting to see a physician