37. Two airplanes are ying in the same direction in adjacent parallel corridors. At time t  0, the rst airplane is 10 km ahead of the second one. Suppose the speed of the rst plane (km/hr) is normally distributed with mean 520 and standard deviation 10 and the second plane s speed, independent of the rst, is also normally distributed with mean and standard deviation 500 and 10, respectively.

a. What is the probability that after 2 hr of ying, the second plane has not caught up to the rst plane?

b. Determine the probability that the planes are separated by at most 10 km after 2 hr.