DETAILS
In a certain city, buses run every 30 minutes on average. At a particular station, buses are scheduled to arrive at 08:00, 08:30, etc. However, because of unpredictable traffic conditions, the actual arrival times are normally distributed about the scheduled arrival times with a standard deviation of 5 minutes. i.e. bus arrival times are N(08:00, 5^2), N(08:30, 5^2), etc.
INTERMEDIATE QUESTION
A passenger, trying to catch the bus, shows up at the station at exactly 08:00. What is his expected waiting time?
HARDER QUESTION
Suppose he shows up at 07:57 (3 minutes before the scheduled arrival time). What is now his expected waiting time?
CHALLENGE QUESTION
At what time must he show up in order to minimize his waiting time?
What would be the worst time to show up (which maximizes his waiting time)?
2007-07-05
05:36:45
·
3 answers
·
asked by
Dr D
7
in
Mathematics