An Air Force intercept squadron consists of 18 planes that s

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.

Solution

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.

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) = (_nC_x) p^x (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

X

P(X)

0

0.0000

1

0.0000

2

0.0000

3

0.0000

4

0.0000

5

0.0000

6

0.0000

7

0.0001

8

0.0008

9

0.0033

10

0.0120

11

0.0350

12

0.0816

13

0.1507

14

0.2153

15

0.2297

16

0.1723

17

0.0811

18

0.0180

Binomial Probabilities Table
	X	P(X)
	0	0.0000
	1	0.0000
	2	0.0000
	3	0.0000
	4	0.0000
	5	0.0000
	6	0.0000
	7	0.0001
	8	0.0008
	9	0.0033
	10	0.0120
	11	0.0350
	12	0.0816
	13	0.1507
	14	0.2153
	15	0.2297
	16	0.1723
	17	0.0811
	18	0.0180