An Air Force intercept squadron consists of 16 planes that should always be read

Question

An Air Force intercept squadron consists of 16 planes that should always be ready for immediate launch. However, there is a probability of 0.25 that the engines of a particular plane will not start at a given attempt. All the planes operate independent of each other. a) What probability distribution would you use and why? b) What is the expected number of planes that will immediately become airborne (meaning engine will start and plane would fly) when the squadron is ordered to launch? c) What is the probability that exactly 12 planes will become airborne? d) What is the probability that at least 14 planes will become airborne?

Explanation / Answer

Solution:-

p = 0.25

1 - p = 0.75

a) We should use binomial distribution as the probability of starting of a plane is independent of the other planes and there are only two outcomes.

b) The expected number of panes that immediately become airborne when squadron is ordered to launch is 4.

E(x) = n × p

E(x) = 4

c) The probability that exactly 12 planes will become airborne is 0.2252.

p = 0.75, n = 16, x = 12

By applying binomial distribution:-

P(x, n, p) = nCx*px *(1 - p)(n - x)

P(x = 12) = 0.2252

d) The probability that atleast 14 planes will become airborne is 0.197.

p = 0.75, n = 16, x = 14

By applying binomial distribution:-

P(x, n, p) = nCx*px *(1 - p)(n - x)

P(x > 14) = 0.197

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