Innocent until proven guilty? In Japanese criminal trials, about 95% of the defe
ID: 3061472 • Letter: I
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†. Suppose you are a news reporter following nine criminal trials.
(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 nine 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.)
(c) As a U.S. news reporter, how many trials n would you need to cover to be at least 99% sure of two or more convictions?
How many trials n would you need if you covered trials in Japan?
Explanation / Answer
a)
In Japan, P(X = 9) = 0.95^9 = 0.6302
In US, P(X = 9) = 0.6^9 = 0.0101
b)
In Japan, E(X) = 9*0.95 = 8.55
In US, E(X) = 9*0.6 = 5.4
In Japan, std. dev. = sqrt(9*0.95*0.05) = 0.6538
In US, std. dev. = sqrt(9*0.6*0.4) = 1.4697