Question

A controlled satellite is known to have an error (distance from target) that is normally distributed with mean zero and standard deviation 4 feet. The manufacturer of the satellite defines a success as a firing in which the satellite comes within 10 feet of the target. Compute the probability that the satellite fails.

Answer 1

the probability that the satellite fails is 0.0124

Explanation:

The manufacturer of the satellite defines a success as a firing in which the satellite comes within 10 feet of the target.

This means that success has the
`(10)/(4)=2.5` standard deviations range in the error distribution.

Z-scores of the Ranges not within -2.5 and 2.5 can be considered as fail and the probability of this is:

P(z>2.5) + P(z<-2.5) = 2 × P(z>2.5) = 2 × 0.0062 = 0.0124