A researcher says that there is a 75% 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 33% 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) = 0.33. 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 67% of the questions were answered with lies, what would you estimate for the actual percentage of lies? (Round your answer to one decimal place.) ______%
A researcher says that there is a 75% 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 33% 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) = 0.33. 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 67% 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
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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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A researcher says that there is a 75% 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 33% 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) = 0.33. Let A = event person is lying, so Ac = event person is not lying. Then
P(A) = __________
(b) If the polygraph indicated that 67% of the questions were answered with lies, what would you estimate for the actual percentage of lies? (Round your answer to one decimal place.)
______%
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) + P(Ac)P(B | Ac)
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 67% 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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