Question

In a certain​ state, about 65​% of drivers who are arrested for driving while intoxicated​ (DWI) are convicted. Complete parts a through c below.

a. If 15 independently selected drivers were arrested for​ DWI, how many of them would you expect to be​ convicted? Choose the correct answer below.

A. 8

B. 7

C. 10

D. 9

b. What is the probability that exactly 10 out of 15 independently selected drivers are​ convicted? The probability that exactly 10 out of 15 drivers are convicted is nothing. ​(Type an integer or decimal rounded to three decimal places as​ needed.)

c. What is the probability that 10 or fewer are​ convicted? The probability that 10 or fewer drivers are convicted is nothing. ​(Type an integer or decimal rounded to three decimal places as​ needed.)

Answer 1

Solution:- Given that n = 15, p = 0.65

a. option C. 10

=> Expect = n*p = 15*0.65 = 9.75 = 10

b. P(X = 10) = 15C10*0.65^10*0.35^5 = 0.2123

c. P(X <= 10) = 0.6481