(1) Most states in the U.S. ban the use of polygraph (“lie-detector”) in their justice sys- tems. False positives (where an individual fails even though he or she is telling the truth) are relatively common and make up about 15% of all test results.(a) If 12 people take a polygraph test, what is the probability that four of the results are false positive?(b) If 12 people take a polygraph test, what is the probability that at least two of the results are false positive?(c) Suppose 100 people take a polygraph test. Find the probability that at most 20 of the results are false positive.

Name: (1) Most states in the U.S. ban the use of polygraph (“lie-detector”)
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Description: (1) Most states in the U.S. ban the use of polygraph (“lie-detector”) in their justice sys- tems. False positives (where an individual fails even though he or she is telling the truth) are relatively common and make up about 15% of all test results.

Given: Probability of success (p) = 0.15 Number of trials (n) = 12 Consider, X be the random…

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(1) Most states in the U.S. ban the use of polygraph (“lie-detector”) in their justice sys- tems. False positives (where an individual fails even though he or she is telling the truth) are relatively common and make up about 15% of all test results.
1. (a) If 12 people take a polygraph test, what is the probability that four of the results are false positive?
2. (b) If 12 people take a polygraph test, what is the probability that at least two of the results are false positive?
3. (c) Suppose 100 people take a polygraph test. Find the probability that at most 20 of the results are false positive.

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