Question

Innocent until proven guilty? In Japanese criminal trials, about 95% of the defendants are found guilty. In the United States, about 60% of the defendants are found guilty in criminal trials. (Source: The Book of Risks, by Larry Laudan, John Wiley and Sons) Suppose you are a news reporter following twelve criminal trials. (For each answer, enter a number.)

(a) If the trials were in Japan, what is the probability that all the defendants would be found guilty? (Round your answer to three decimal places.)

What is this probability if the trials were in the United States? (Round your answer to three decimal places.)

(b) Of the twelve trials, what is the expected number of guilty verdicts in Japan? (Round your answer to two decimal places.)

What is the expected number in the United Sates? (Round your answer to two decimal places.)

What is the standard deviation in Japan? (Round your answer to two decimal places.)

What is the standard deviation in the United States? (Round your answer to two decimal places.)

Answer 1

Page Solutions - 5 @ Here we use NI On Japanese cuiminal feials. 95.7.06 the defendants aree frend guilt 27.(220.95 In United states about 604.85 the defendants are found guib (p= 0.60) binomiou distuibution because no. of trial us finite and probability of succes is comtenti X~ defendant found gilty in japanese yw defendants found guilty in U.S. X&Y both are binomialy distributed. n =12 defended Probability that au Japanese found guilttitis PLX512): 12 10.95)"210.0510 1 19 11 (12 0.54036 ñ 0.540 Probability that all UiS defended found guits us PLYE12) 12 Lan (0.62 10.40 = 0.002176 ~ 0.002

Dl Expected no. of guilt in 12 teicies El Japan) - bbt 12x0.95 = 11.40 Elu.s) = npz nb2 12x0.60 = 7:20 Standard deviation o L Japan) = supiltapo J12x0.95 x 0.05 0.75498 ~ 0.75 -(0.5) hbz t-p2) J 12x06x0.4 E 1,69705 1,70