An autopilot attempts to maintain an airplane's altitude at a constant 18000 feet. because of random variations, the actual altitude x is a normal random variable with mean 18000 feet and variance=2500 feet2 . (a) what is the probability that the altitude differs from the assigned 18000 value by more than 100 feet? (b) suppose that by mechanically improving the autopilot, the variance of the airplane's altitude can actually be reduced. find the value of the variance such that the probability that the altitude differs from the assigned 18000 value by more than 100 feet is at most 0.01