Question

X-games star "Mad Mark" likes to do back flips on his motorbike. Assume his travel distance off the launch ramp is normally distributed with a mean of 150 feet and standard deviation of 10 feet. Assume that the landing ramp at the other end is 30 feet long and that he can land anywhere on the 30 foot ramp and be okay.

To maximize Mark's probability of landing on the ramp how far from the end of the launch ramp should the landing ramp start?

Given the answer from the first question above, what is the probability he will land on the landing ramp (i.e. not break any bones)?

Answer 1

1. For maximum probability of landing on the ramp, 150 feet from the end of the launch ramp should the landing start.

2. The probability that Mad Mark will land on the landing ramp is 0.498.

Calculation of above two parts is given in the attached file.