An article states that false-positives in polygraph tests (i.e., tests in which an individual fails even though he or she is telling the truth) are relatively common and occur about 10% of the time. Suppose that such a test is given to 10 trustworthy individuals. (Round all answers to four decimal places.)

(a) What is the probability that all 10 pass?

P(X = 10) =___________

(b) What is the probability that more than 2 fail, even though all are trustworthy?

P (more than 2 fail, even though all are trustworthy) = _______________

(c) The article indicated that 600 FBI agents were required to take a polygraph test. Consider the random variable x = number of the 600 tested who fail. If all 600 agents tested are trustworthy, what are the mean and standard deviation of x?

Mean =

Standard deviation =