An autopilot attempts to maintain an airplaneSolutiona What

An autopilot attempts to maintain an airplane

Solution

(a) What is the probability that the altitude differs from the assigned 18000 value by more than 100 feet?

P(|X-mean|>100) = P(X-mean<-100)+ P(X-mean>100)

=P((X-mean)/s <-100/sqrt(2500)) + P((X-mean)/s >-100/sqrt(2500))

=P(Z<-2)+ P(Z>2) =0.0455 (from standard normal table)

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(b) Suppose that by mechanically improving the autopilot, the variation of the airplane