A heart specialist schedules 16 patients each day, 1 every 30 minutes, starting at 9 A.M. Patients are expected to arrive for their appointments at the scheduled times. However, past experience shows that 10% of all patients arrive 15 minutes early, 25% arrive 5 minutes early, 50% arrive exactly on time, 10% arrive 10 minutes late, and 5% arrive 15 minutes late. The time the specialist spends with a patient varies, depending on the type of problem. Analysis of past data shows that the length of an appointment has the distribution in the following table.

lenght of appointment	probability
24	0.20
27	0.25
30	0.30
33	0.10
36	0.10
39	0.05

Simulate the system for 200 days to calculate the following performance measures:

a. The probability that a patient will not wait in the queue.

b. The probability that the last patient will not wait in the queue.

c. The utilization of the specialist