A lawyer 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. (a) What is the probability that a trip will take at least ½ hour?
(b) If the office opens at 9:00 A. M. and he leaves his house at 8:45 A. M. daily, what percentage of the time is he late for work?
(c) If he leaves the house at 8:35 A. M. and coffee is served at the office from 8:50 A. M. until 9:00 A. M., what is the probability that he misses coffee?
​(d) Find the length of time above which we find the slowest 10​% of trips.
(e) Find the probability that 2 of the next 3 trips will take at least one half
1/2 hour.