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 twelve 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 twelve trials, what is the expected number of guilty verdicts in Japan?  verdicts What is the expected number in the United Sates?  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, what is the smallest number of trials n you would need to cover to be at least 99% sure of two or more convictions?  trials What is the smallest number of trials n you would need if you covered trials in Japan?  trials

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.