An article states that false-positives in polygraph tests (i.e., tests in which

Question

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 15% 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 400 FBI agents were required to take a polygraph test. Consider the random variable x = number of the 400 tested who fail. If all 400 agents tested are trustworthy, what are the mean and standard deviation of x?
Mean = 3
Standard deviation = 4

Explanation / Answer

a) .85^10= 0.197 b) 0 fail = .197 1 fail 10!/9!*1! .15* .85^9= .347 2 fail 10!/8!*2! .15^2*.85*8= .276 More than 2= 1-.197-.276-.347= 0.18 c) Mean = 400*.15= 60 standard deviation= sqrt 400*.85*.15= 7.14

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