Question

Of all the registered automobiles in a city, 11% fail the emissions test. Twelve automobiles are selected at random to undergo an emissions test. Round the answers to four decimal places.

Answer 1

Complete question :

Of all the registered automobiles in a city, 11% fail the emissions test. Twelve automobiles are selected at random to undergo an emissions test. Round the answers to four decimal places.

1.)Probability that exactly 3 fail

2.) Fewer Than 3 fail

Answer:

0.1026 ;

0.8623

Explanation:

Using the binomial probability formula :

P(x =x) = nCx * p^x * (1 - p)^(n - x)

p = 0.11

1 - p = 1 - 0.11 = 0.89

n = 12

P(x = 3) = 12C3 * 0.11^3 * 0.89^0

P(x = 3) = 0.1026

Fewer Than 3

P(x < 3) = p(x = 0) + p(x = 1) + p(x = 2)

Using a binomial probability calculator :

P(x = 0) = 0.2470

P(x = 1) = 0.3663

P(x = 2) = 0.2490

(0.2470 + 0.3663 + 0.2490) = 0.8623