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

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

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

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


(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?
trials

How many trials n would you need if you covered trials in Japan?
trials

Answer 1

a) If the trials were in Japan, what is the probability that all the defendants would be found guilty =0.95¹⁰ =0.599

this probability if the trials were in the United States =0.60¹⁰ =0.006

b)

expected number of guilty verdicts in Japan =10*0.95=9.5

expected number in the United Sates =10*0.6 =6

standard deviation in Japan =sqrT(np(1-p))=sqrt(10*0.95*0.05)=0.6892

standard deviation in the United States =sqrt(10*0.6*0.4)=1.5492

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

=3 trails

How many trials n would you need if you covered trials in Japan? =8 trails