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 five 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 five 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

Answer:

a)

probability that all the defendants would be found guilty =(0.95)5 =0.773781

probability if the trials were in the United States =(0.6)5 =0.07776

b)

expected number of guilty verdicts in Japan=np=5*0.95=4.75

expected number in the United Sates =5*0.6=3

std deviation of guilty verdicts in Japan =(np(1-p))1/2 =0.48734

std deviation of guilty verdicts in US =(np(1-p))1/2 =1.0954

c)

here probability of 2 or more convict out of n =P(X>=2) >0.99

1-P(X<=1)>0.99

P(X<=1)<0.01

from binomcdf function of TI-84; for US n =8

for Japan n =3