Question: 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 12 criminal trials in the USA.

a. What is the expected number of guilty verdicts? That is, find the mean number of guilty verdicts for this group of 12 trials.

b. Calculate the standard deviation for this distribution.

c. Calculate the probability that fewer than half of the cases will result in guilty verdicts. That is, find the probability that fewer than 6 of the defendants will be found guilty.

d. Calculate the probability that at least one of the trials results in a guilty verdict.

e. In Japanese criminal trials, about 95% of the defendants are found guilty. (Source: The Book of Risks, by Larry Laudan, John Wiley and Sons). If you are following 7 criminal trials in Japan, what is the probability that 5 of them result in guilty verdicts?