(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…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

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.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 6 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Propositional Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions