Instructor-created question Question Help Lie detectors are controversial instru

Question

Instructor-created question Question Help Lie detectors are controversial instruments, barred from use as evidence in many courts. Nonetheless, many employers use lie detector screening as part of their hiring process. There has been some research, but no agreement, about the reliability of polygraph tests. Based on this research, suppose that a polygraph can detect 67% of lies, but incorrectly identifies 23% of true statements as lies. A company believes that 89% of its job applicants are trustworthy The company gives everyone a polygraph test, asking "Have you ever stolen anything from your place of work?" Naturally, all the applicants answer "No," but the polygraph identifies some of those answers as lies, making the person ineligible for a job. A hint: The statement a polygraph can detect x% of lies is really a conditional probability given that a person lies, x% of the time the machine reports "Lie a) What is the probability that a random job applicant will be an honest worker who is cleared by the polygraph? The probability that a random job applicant is an honest worker who is cleared by the polygraph is .6853 Type an integer or a decimal.) b) What is the probability that a job applicant who is rejected by the polygraph was actually dishonest? The probability that a job applicant who is rejected by the polygraph was actually dishonest is 2637 Round to four decimal places as needed.)

Explanation / Answer

a)

P(cleared by polygraph)=P(honest and cleared by polygraph)+P(not honest and cleared by polygraph)

=0.89*(1-0.23)+(1-0.89)*(1-0.67)=0.7216

hence P(honest worker given cleared by polygraph)

=P(honest and cleared by polygraph)/P(cleared by polygraph)=0.89*(1-0.23)/0.7216=0.9497

b)

P(dishnest |not  cleared by polygraph)

=P(dishonest and not cleared by polygraph)/P(not cleared by polygraph)

=(1-0.89)*0.67/(1-0.7216)=0.2647

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.