Chapter 12.4, Problem 29E

Time of a commute A student with an eight o’clock class at the University of Maryland commutes to school by car. She has discovered that along each of two possible routes her traveling time to school (including the time to get to class) is approximately a normal random variable. If she uses the Capital Beltway for most of her trip, $\mu =25$ minutes and $\sigma =5$ minutes. If she drives a longer route over local city streets, $\mu =28$ minutes and $\sigma =3$ minutes. Which route should the student take if she leaves home at $7:30\text{A}\text{.M}\text{.}$? (Assume that the best route is one that minimizes the probability of being late to class.)