Probability and Stats

I would approach the problems by using a binomial distribution (more info here: https://www.khanacademy.org/math/statistics-probability/random-variables-stats-library/binomial-random-variables/v/binomial-distribution). 

Let a false detection (the machine shows that a truthful person is lying) be a success and a correct detection (the machine shows that a truthful person is telling the truth) be a failure. This way, your p is 0.2 (the probability of a success), your n is 12 (the number of people given the lie detector test), and your x (or k) is however many people are supposed to be falsely accused of lying. 

Plug that into the binomial distribution formula to answer your first two questions.

For the last question, you could get the probabilities of each value of x/k and calculate the mean and standard deviation of the distribution by treating them like data points.