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 six 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 six 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.)

Answer 1

a)

Here, n = 6, p = 0.6, (1 - p) = 0.4 and x = 6
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 6)
P(X = 6) = 6C6 * 0.6^6 * 0.4^0
P(X = 6) = 0.047

Here, n = 6, p = 0.95, (1 - p) = 0.05 and x = 6
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 6)
P(X = 6) = 6C6 * 0.95^6 * 0.05^0
P(X = 6) = 0.735
0

b)

Here, μ = n*p
= 6 * 0.60
= 3.60,

Here, μ = n*p

= 6 * 0.95
= 5.70,

c)

σ = sqrt(np(1-p)) = 1.20

σ = sqrt(np(1-p)) = 0.53