Question

According to U.S. Department of Transportation report, 8% of all the registered cars fail the emissions test.

(a) For a random sample of 10 cars, what is the chance that 4 of them will fail the test?

b) how many of them are expected to fail the test?

(c ) For a random sample of 10 cars, find the probability that more than8 of them will fail the test?

Answer 1

We have

p = probability that registered car fail the test = 0.08

a) let X : number of registered car will fail

n = sample size = 10

We asked P( X = 4)

Using binomial probability

P( X = 4) = n!/X! * (n - X)! * p​​​​​​X​​​​​ *( 1- p) n -x

P( X = 4)= 10! /4!*6! *(0.08)4*(0.92)6

P( X = 4) = 0.0052

b) expected number of cars fail the test

E( X ) = n * p = 10 *0.08

E( X ) = 0.8

c) P( X > 8 ) = P( X = 9 ) + P( X = 10)

P( X = 9) = 10!/9!*1! * (0.08)9* (0.92)1 = 0.0000

P( X = 10) = 10!/10!*0! *(0.08)10*(0.92)0 = 0.0000

P( X > 8 ) = 0.0000 + 0.0000

P( X > 8) = 0.0000