Question

In a certain​ state, about 70 70​% of drivers who are arrested for driving while intoxicated​ (DWI) are convicted. Complete parts a through c below.

a. If 12 12 independently selected drivers were arrested for​ DWI, how many of them would you expect to be​ convicted?

Choose the correct answer below.

A. 6

B. 9

C. 7

D. 8

Your answer is correct. b

What is the probability that exactly 8 out of 12 independently selected drivers are​ convicted? The probability that exactly 8 out of 12 drivers are convicted is nothing . ​(Type an integer or decimal rounded to three decimal places as​ needed.)

Answer 1

We have given -

P = 0.70 , n = 12

So expected value = E(X) = n * p = 0.70 * 12 = 8.4  

But as this is the expected number of drivers who are convicted this would be integer ( as it is number of drivers )

So By rounding to the next whole integer. We get-

Expected value = E(X) = 9

Hence B. 9 is the correct answer.

The probability that exactly 8 out of 12 drivers are convicted is 0.231

Hope this will help you. Thank you :)