An article states that false-positives in polygraph tests (tests in which an ind

Question

An article states that false-positives in polygraph tests (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 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 =  
Standard deviation =

Explanation / Answer

a) 0.9010= 0.349
b) 0 fail = .349
1 fail 10!/9!*1! .10* .0.9^9= .387
2 fail 10!/8!*2! .10^2*.9*8= .194
More than 2= 1-.194-.387-.349= 0.07
c) Mean = 400*.10= 40
standard deviation= sqrt 400*.90*.1= 6

Hope this will helps you. Thanks and God Bless You :-)

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