Question

In: Statistics and Probability

Innocent until proven guilty? In Japanese criminal trials, about 95% of the defendants are found guilty....

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. (Source: The Book of Risks, by Larry Laudan, John Wiley and Sons) Suppose you are a news reporter following twelve criminal trials. (For each answer, enter a number.)

(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? (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

*I am needing help inputting this equation(s) into Excel

Solutions

Expert Solution

Given that

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.

Binomial distribution formula

p = Probability of success

q = 1-p Probability of failure

a)

Trails were in Japan,

p = 0.95 and q = 0.05

n = 12

All the defendants would be found guilty, So r = 12

Then the probability is

Trails were in U.S ,

p = 0.60 and q = 0.40

n = 12

All the defendants would be found guilty, So r = 12

Then the probability is

b)

Expected number of guilty verdicts in Japan

n = 12, p = 0.95

= 12 * 0.95

= 11.4

Expected number of guilty verdicts in U.S

n = 12, p = 0.60

= 12 * 0.60

= 7.2

Standard deviation in Japan

n = 12, p = 0.95 , q = 0.05

= sqrt( 12*0.95*0.05)

= 0.75

Standard deviation in U.S

n = 12, p = 0.60 , q = 0.40

= sqrt( 12*0.60*0.40)

= 1.70

orchestra answered 1 year ago
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