Answered: A researcher says that there is a 76%…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A researcher says that there is a 76% chance a polygraph test (lie detector test) will catch a person who is, in fact, lying. Furthermore, there is approximately a 5% chance that the polygraph will falsely accuse someone of lying.

(a) If the polygraph indicated that 38% of the questions were answered with lies, what would you estimate for the actual percentage of lies in the answers? Hint: Let B = event detector indicates a lie. We are given P(B) = 0.38. Let A = event person is lying, so A^c = event person is not lying. Then

P(B) = P(A and B) + P(A^c and B)
P(B) = P(A)P(B | A) + P(A^c)P(B | A^c)

Replacing P(A^c) by 1 − P(A) gives

P(B) = P(A) · P(B | A) + [1 − P(A)] · P(B | A^c)

Substitute known values for P(B), P(B | A), and P(B | A^c) into the last equation and solve for P(A). (Round your answer to two decimal places.)
P(A) =

(b) If the polygraph indicated that 62% of the questions were answered with lies, what would you estimate for the actual percentage of lies? (Round your answer to one decimal place.)

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