The table below contains the results from experiments with a polygraph instrumen

Question

The table below contains the results from experiments with a polygraph instrument. If four of the test subjects are randomly selected without replacement, find the probability that, in each case, the polygraph indicated that the subject lied. Is such an event unusual? Positive test result (Positive test Indicated that the subject lied.) Negative test result (Polygraph test Indicated that the subject did not lie.) What is the probability? (Round to three decimal places as needed.) Is such an event unusual? No (Did Not Lie) Yes (Lied) 13 34 (false positive) (true positive) 24 5 (true negative) (false negative) Click to select your answer(s).

Explanation / Answer

Total number of subjects: 13+34+24+5 = 76

Out of these 76 subjects, in 34+5 =39 cases test indicates that subject lied. So the probability that test indicate "subject lie" is

P(lie) = 39 /76 = 0.5132

Since subjects are independent so the probability that for all four test indicate subject lie is

0.5132 *0.5132 *0.5132* 0.5132 = 0.0693659902955776

Hence, answer: 0.069

No it is not unusal because this probability is greater than 0.05.

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