EXAMPLE 5.13

Getting to and from campus. You live off campus and take the shuttle, provided by your apartment complex, to and from campus. Your time on the shuttle in minutes varies from day to day. The time going to campus X has the N(20,4) distribution, and the time returning from campus Y varies according to the N(18, 8) distribution. If they vary independently, what is the probability that you will be on the shuttle for less time going to campus?

The difference in times X − Y is Normally distributed, with mean and variance

μ_X−Y = μ_X − μ_Y = 20 − 18 = 2

Because , X − Y has the N(2, 8.94) distribution. Figure 5.12 illustrates the probability computation:

P(X < Y) = P(X − Y < 0)

= P(Z < −0.22) = 0.4129

Although, on average, it takes longer to go to campus than return, the trip to campus will take less time on roughly two of every five days.