57. Let X and Y be the times for a randomly selected individual to complete two different tasks, and assume that (X, Y ) has a bivariate normal distribution with mX  100, sX  50, mY  25, sY  5, r  .5. From statistical software we obtain P(X100, Y25)

.3333, P(X  50, Y  20)  .0625, P(X  50, Y  25)  .1274, and P(X  100, Y  20)  .1274.

a. Find P(50  X  100, 20  Y  25).

b. Leave the other parameters the same but change the correlation to r  0 (independence). Now recompute the answer to part (a). Intuitively, why should the answer to part

(a) be larger?