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Lie detector test. The software for a lie detector based
Chapter 3, Problem 72E(choose chapter or problem)
Lie detector test. The software for a lie detector based on voice stress levels—called the computerized voice stress analyzer (CVSA)—is available for about $10,000. The manufacturer claims that the CVSA is 98% accurate, and, unlike a polygraph machine, will not be thrown off by drugs and medical factors. However, laboratory studies by the U.S. Defense Department found that the CVSA had an accuracy rate of 49.8%—slightly less than pure chance. Suppose the CVSA is used to test the veracity of four suspects. Assume the suspects’ responses are independent.
a. If the manufacturer’s claim is true, what is the probability that the CVSA will correctly determine the veracity of all four suspects?
b. If the manufacturer’s claim is true, what is the probability that the CVSA will yield an incorrect result for at least one of the four suspects?
c. Suppose that in a laboratory experiment conducted by the U.S. Defense Department on four suspects, the CVSA yielded incorrect results for two of the suspects. Use this result to make an inference about the true accuracy rate of the lie detector.
Questions & Answers
QUESTION:
Lie detector test. The software for a lie detector based on voice stress levels—called the computerized voice stress analyzer (CVSA)—is available for about $10,000. The manufacturer claims that the CVSA is 98% accurate, and, unlike a polygraph machine, will not be thrown off by drugs and medical factors. However, laboratory studies by the U.S. Defense Department found that the CVSA had an accuracy rate of 49.8%—slightly less than pure chance. Suppose the CVSA is used to test the veracity of four suspects. Assume the suspects’ responses are independent.
a. If the manufacturer’s claim is true, what is the probability that the CVSA will correctly determine the veracity of all four suspects?
b. If the manufacturer’s claim is true, what is the probability that the CVSA will yield an incorrect result for at least one of the four suspects?
c. Suppose that in a laboratory experiment conducted by the U.S. Defense Department on four suspects, the CVSA yielded incorrect results for two of the suspects. Use this result to make an inference about the true accuracy rate of the lie detector.
ANSWER:Solution:
Step 1 of 3:
Given the manufacturer claim that the CVSA is 98%.
Let A = CVSA correctly determine the veracity of a suspect's.
Then, P(A) = 98% = 0.98
a). To find the probability that the CVSA will correctly determine the veracity of all four suspects.
Thus,
= 0.9224
Therefore, the probability that the CVSA will correctly determine the veracity of all four suspects is 0.9224.