Norris Medical Clinic is staffed by a single physician who, on average, requires 15 minutes to treat a patient. The distribution of this service time follows a truncated normal distribution with a standard deviation of 4 minutes and a minimum value of 5 minutes. Patients arrive at the clinic according to the following probability distribution: Time between arrivals (minutes) Probability 5 0.09 10 0.15 15 0.23 20 0.38 25 0.08 30 0.07 (a) Simulate 100 patient arrivals using spreadsheet. For each patient, show the time between arrival, arrival time, service start time, service time, service end time, and waiting time. (20 marks) (b) Based on 1 replication, (i) What is the average waiting time per patient? (ii) What percentage of patients need to wait for more than 15 minutes before service starts? (6 marks) (c) Replicate the above simulation for 200 times using Data Table. (7 marks) (d) Based on 200 replications, (i) What is the average waiting time per patient? (ii) On average, what percentage of patients need to wait for more than 15 minutes before service starts? (iii) Develop a relative frequency table for the average waiting time per patient. Use class intervals with the upper limits 5 minutes, 10 minutes, 15 minutes, 20 minutes, 25 minutes, 30 minutes, and more than 30 minutes. (iv) Plot a chart for the relative frequency table in part (iii), label everything clearly. (17 marks) - End -