Problem 5E

Of all the registered automobiles in a certain state, 10% violate the state emissions standard, Twelve automobiles are selected at random to undergo an emissions test.

a. Find the probability that exactly three of them violate the standard.

b. Find the probability that fewer than three of them violate the standard.

c. Find the probability that none of them violate the standard.

Answer :

Step 1 of 4 :

Given,we have the data of registered automobiles in a certain state, 12 automobiles are selected at random to undergo an emission test, 10% violate the state emissions standard.

Let X follows binomial distribution with probability mass function is

P(x: n,p) = (1 - p , x = 0, 1, 2, ….., n.

Mean of the binomial distribution is

= np

Variance of the binomial distribution is

= npq

Where, n = 12 and p = 10% = 0.10