An Air Force intercept squadron consists of 18 planes that should always be read

ID: 3024072 • Letter: A

Question

An Air Force intercept squadron consists of 18 planes that should always be ready for immediate launch. However, a plane’s engines are troublesome, and there is a probability of 0.20 that the engines of a particular plane will not start at a given attempt. Assume the planes are independent. The squadron commander is interested in how many planes will immediately become airborne if the squadron is scrambled.

a. Find the expected number of planes that will immediately become airborne if the squadron is scrambled.

b. Find the probability that exactly 11 planes launch successfully.

c. Find the probability that more than 14 planes launch successfully.

Explanation / Answer

probability of 0.20 that the engines of a particular plane will not start

probability that the engines of a particular plane will start = 1-0.2=0.8

n=18

Expectation = np =18*0.8 = 14.4

P(X=x) = (nCx) px (1-p)n-x

P( x=11) = 0.035

c. Find the probability that more than 14 planes launch successfully.

P( x >14) = 0.501

Binomial Probabilities Table

P(X)

0.0000

0.0001

0.0008

0.0033

0.0120

0.0350

0.0816

0.1507

0.2153

0.2297

0.1723

0.0811

0.0180