(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”)
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
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 variable that follows the binomial distribution with n= 12(a) The probability that four of the results are false positive is calculated as follows: P(X=4)=12C4×(0.15)4×(1-0.15)12-4 =12!(12-8)!4!×(0.15)4×(1-0.15)8=0.0682 Thus, the probability is 0.0682.(b) The probability that at least two of the results are false positive could be calculated as: PX≥2=1-PX<2=1-PX<0+PX<1=1-12C0×(0.15)0×(1-0.15)12-0 +12C1×(0.15)1×(1-0.15)12-1 =1-0.1422+0.3012=0.5566 Thus, the required probability is 0.5566(c) Here, Number of trials (n) = 100 Probability of success (p) = 0.15 In this case, np=100(0.15)=15>5n1-p=100(1-0.15)=85>5 Since, np >5 and n(1-p) >5 Thus, normal approximation to binomial distribution is to be used here. The mean and standard deviation are: Meanμ=n×p=1000.15=15Standard deviation(σ)=n×p×(1-p)=100×0.15×(1-0.15)=3.571The probability that at most 20 of the results are false positive could be calculated as follows: PX≤20=Px-μσ≤20+0.5-μσ=PZ<20.5-153.571=P(Z<1.5402)=0.9382 Hence, the probability is 0.9382.

Answered: (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…

MATLAB: An Introduction with Applications

6th Edition

ISBN: 9781119256830

Author: Amos Gilat

Publisher: John Wiley & Sons Inc

See similar textbooks

Concept explainers

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

Topic Video

Question

(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.