A researcher says that there is a 78% 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 35% 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) = 0.35. Let A = event person is lying, so Ac = event person is not lying. Then P(B) = P(A and B) + P(Ac and B) P(B) = P(A)P(B | A) + P(Ac)P(B | Ac) Replacing P(Ac) by 1 − P(A) gives P(B) = P(A) · P(B | A) + [1 − P(A)] · P(B | Ac) Substitute known values for P(B), P(B | A), and P(B | Ac) into the last equation and solve for P(A). (Round your answer to two decimal places.) P(A) = (b) If the polygraph indicated that 65% of the questions were answered with lies, what would you estimate for the actual percentage of lies? (Round your answer to one decimal place.) %

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
Question

A researcher says that there is a 78% 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 35% 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) = 0.35. Let A = event person is lying, so Ac = event person is not lying. Then
P(B) = P(A and B) + P(Ac and B)
P(B) = P(A)P(B | A) + P(Ac)P(B | Ac)
Replacing P(Ac) by 1 − P(A) gives
P(B) = P(A) · P(B | A) + [1 − P(A)] · P(B | Ac)
Substitute known values for P(B), P(B | A), and P(B | Ac) into the last equation and solve for P(A). (Round your answer to two decimal places.)
P(A) =

(b) If the polygraph indicated that 65% of the questions were answered with lies, what would you estimate for the actual percentage of lies? (Round your answer to one decimal place.)
%

 

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Discrete Probability Distributions
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
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman