Alawyer commutes daily from his suburban home to his midtown office. the average time for a one-way trip is 27 minutes, with a standard deviation of 3.7 minutes. assume the distribution of trip times to be normally distributed. complete parts (a) through (e) below.
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.