1)

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 followingfivecriminal 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 thefivetrials, what is the expected number of guilty verdicts in Japan?

What is the expected number in the United Sates?

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.)

2)

USA Todayreported that approximately 25% of all state prison inmates released on parole become repeat offenders while on parole. Suppose the parole board is examining five prisoners up for parole. Letx= number of prisoners out of five on parole who become repeat offenders.

x p(x)

0 0.229

1 0.385

2 0.210

3 0.130

4 0.045

5 0.001

(a) Find the probability that one or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.)

How does this number relate to the probability that none of the parolees will be repeat offenders?

(b) Find the probability that two or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.)

(c) Find the probability that four or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.)

(d) Compute, the expected number of repeat offenders out of five. (Round your answer to three decimal places.)

=

(e) Compute, the standard deviation of the number of repeat offenders out of five. (Round your answer to two decimal places.)

=