95% Japan, 60% US, 4 criminal trials. What is the standard deviation in Japan, and US?(Round your answer to two decimal places.)

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 four criminal trials.

 

Answer 1

To answer this, we need to assume a particular distribution, so let’s use the binomial distribution with p as the probability and n as the number of trials=4.

The mean is np and the variance is np(1-p). So np=4*0.95=3.80 in Japan and 4*0.60=2.40 in the US.

The variances are 3.80*0.05=0.19 in Japan and 2.40*0.4=0.96 in US.

The standard deviations are the square roots of the variances: 0.44 in Japan and 0.98 in US.

Japan: 3.80±0.44, US: 2.40±0.98