At a bungy jumping facility, the bungy cord has just been replaced. It is known that the effective stiffness of the bungy cord is uniformly distributed between 2 and 4 lbs/ft. Suppose that the next jumper weighs 160 lbs. The water surface is 70 ft down. Assuming that the distance the next jumper falls is equal to his or her weight divided by the effective cord stiffness, a) derive the distribution of the falling distance and compute the probability that the next jumper will get wet, b) derive a second order approximation to the mean of the next jumper's falling distance. Compare this approximation to the exact value obtained using the distribution of part (a)