1. [Module d: 20 Points]According to The Globe and Mail (OCTOBER 5, 2020), Private medical clinics are offering COVID-19 tests to Canadians willing to pay a fee to circumvent lengthy lineups at government sites and long waits for results from laboratories. The for-profit clinics serve individual patients as well as companies that require employees to test negative for the coronavirus before returning to work. Individuals pay anywhere from $50 to $250 for a test. Suppose that, on a typical Monday, an average of 20 patients per hour arrive at a private COVID-19 testing center. There is one nurse at the center, and the average time required to take a sample is 2 minutes. It is assumed that service times may be described by the exponential distribution. A single line would be used, and the patient at the front of the line would go to the first available nurse. If a single nurse is used, find:
   1. What is the average time spent waiting in the queue? What is the average time spent in the system?
   2. What is the average number of patients waiting in the queue? What is the average number of patients in the system?
   3. What is the probability that the testing center is empty? What percentage of the time is the nurse busy?
   4. What is the probability that there are exactly five patients in the system? What is the probability that there are more than five patients in the system?
   5. The cost of the nurse is $40 per hour, but because of patients balking and reneging, the test center loses about $50 per hour of customer time spent waiting for the nurse to take a sample. Calculate the total queuing costs (i.e., service cost and patients waiting cost). The test centre operates 12 hours per day.