Dr. T Practices dentistry in International Falls, Minnesota. T tries hard to schedule appointments so that patients do not have to wait beyond their appointment time. His August 21 schedule is shown in the following table.
SCHEDULED APPOINTMENT AND TIME EXPECTED TIME NEEDED
ADAMS 9:30 AM 15
BROWN 9:45 AM 20
CRAWFORD 10:15 AM 15
DANNON 10:30 AM 10
EARVING 10:45 AM 30
FINK 11:15 AM 15
GRAHAM 11:30 AM 20
HINKEL 11:45 AM 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, while some take less time.
T's experience dictates the following:
? 20% of the patients will be 20 minutes early.
? 10% of the patients will be 10 minutes early.
? 40% of the patients will be on time.
? 25% of the patients will be 10 minutes late.
? 5% of the patients will be 20 minutes late.
He further estimates that:
? 15% of the time he will finish in 20% less time than expected.
? 50% of the time he will finish in the expected time.
? 25% of the time he will finish in 20% more time than expected.
? 10% of the time he will finish in 40% more time than expected.
Dr. T has to leave at 12:15 PM on August 21 to catch a flight to a dental convention in San Francisco. Assuming that he is ready to start his workday at 9:30 AM and that patients are treated in order of their scheduled exam (even if one late patient arrives after an early one), will he be able to catch the flight? Comment on his situation after performing an expected value analysis.
This solution exemplifies expected value.