Problem 4 (Dr. Greenberg)

Dr. Mark Greenberg practices dentistry in Topeka, Kansas. Greenberg tries hard to schedule appointments so that patients do not have to wait beyond their appointment time. His October 20 schedule is shown in the following table.

Scheduled Appointment	Time	Expected Time Needed
Adams	09:30 a.m.	15
Brown	09:45 a.m.	20
Crawford	10:15 a.m.	15
Dannon	10:30 a.m.	10
Erving	10:45 a.m.	30
Fink	11:15 a.m.	15
Graham	11:30 a.m.	20
Hinkel	11:45 a.m.	15

Unfortunately, not every patient arrives exactly on schedule, and expected times to examine patients are just that---expected. Some examinations take longer than expected, and some take less time. Greenbergs experience dictates the following:

1. 20% of the patients will be 20 minutes early.
2. 10% of the patients will be 10 minutes early.
3. 40% of the patients will be on time.
4. 25% of the patients will be 10 minutes late.
5. 5% of the patients will be 20 minutes late.

He further estimates that

1. 15% of the time he will finish in 20% less time than expected.
2. 50% of the time he will finish in the expected time.
3. 25% of the time he will finish in 20% more time than expected.
4. 10% of the time he will finish in 40% more time than expected.

Dr. Greenberg has to leave at 12:15 p.m. to catch a flight. Assuming that he is ready to start his work at 9:30 a.m. and that patients are treated in order of their scheduled appointment (even if one late patient arrives before an early one), what is the probability that he will be able to make the flight? Please build an Excel model to solve the problem and estimate the probability by repeating the simulation 1,000 times.