An engineer commutes daily from his suburban home to his midtown office. The average time for a one way trip is 24 minutes, with a standard deviation of 3.8 minutes. Assume the distribution of trip times to be normally distributed.
What is the probability that a trip will take at least 30 minutes?
If the commuting engineer should be at the office at 9:00 AM and he leaves his house at 8:40 AM every day, what fraction of the time is he late for work?
The engineer doesn't want to leave too early, either, because he likes to work out in the morning. His optimal situation would be to arrive no more than 5 minutes late, or more than 10 minutes early. What is the maximum probability that he can fall within this zone if he chooses a fixed time to leave every day?