Question
In: Statistics and Probability
. A lie detector will show a positive reading 10% of the time when a person...
. A lie detector will show a positive reading 10% of the time when a person is really telling the truth, and a lie detector will show a positive reading 90% of the time when a person is in fact lying. The lie detector is tested on three subjects. The first subject is (secretly) known to lie to every single question, no matter what the question (Remind you of anyone?). The second lies to 70% of all questions, and the third lies to 10% of all questions.
a. What is the probability that the lie detector shows a positive on all three subjects?
b. What is the probability that the lie detector shows a negative on all three subjects?
c. What is the probability the lie detector shows a positive on the first subject and a negative on the other two subjects?
d. Given that the lie detector showed a positive result on exactly one subject, what is the probability that subject was the first one?
e. Given that the lie detector showed a positive result on exactly two subjects, what is the probability those two subjects were subjects 1 and 2?
f. Given that the third subject told the truth, what is the probability the lie detector incorrectly concludes he lied? This is called a false positive reading.
Solutions
orchestra answered 2 years agoRelated Solutions
Lie Detector: Suppose a lie detector allows 20% of all lies to go undetected. (a) If...
Lie Detector: Suppose a lie detector allows 20% of all lies to
go undetected.
(a) If you take the test and tell 10 lies, what is the
probability of having 5 or more go undetected? Round your answer to
3 decimal places.
(b) Would 5 undetected lies be an unusually high number* of
undetected lies? Use the criteria that a number (x) is unusually
large if P(x or more) ≤ 0.05.
-Yes, that is an unusually high number of undetected...
A new lie-detector machine is invented and tested. When test subjects lie, the machine catches 86%...
A new lie-detector machine is invented and tested. When test
subjects lie, the machine catches 86% of them in a lie. When test
subjects tell the truth, the machine thinks that 6% of them lie. A
local police department begins to use this lie-detector machine in
interrogations. Suppose that 15% of people arrested lie in their
interrogations. The police interrogated a subject and the machine
indicated that the person was telling the truth. What is the
probability that the subject...
A POLYGRAPH (LIE DETECTOR) IS AN INSTRUMENT USED TO DETERMINE IF AN INDIVIDUAL IS TELLING THE...
A POLYGRAPH (LIE DETECTOR) IS AN INSTRUMENT USED TO DETERMINE IF
AN INDIVIDUAL IS TELLING THE TRUTH. THESE TESTS ARE CONSIDERED TO
BE 95 % RELIABLE. IN OTHER WORDS, IF AN INDIVIDUAL LIES, THERE IS A
.95 PROBABILITY THAT THE TEST WILL DETECT A LIE. LET THERE ALSO BE
A .025 PROBABILITY THAT THE TEST ERRONEOUSLY DETECTS A LIE EVEN
WHEN THE INDIVIDUAL IS ACTUALLY TELLING THE TRUTH. CONSIDER THE
NULL HYPOTHESIS, "THE INDIVIDUAL IS TELLING THE TRUTH, THE ANSWER...
suppose a police detective is about to administer a polygraph (lie detector) test on an "individual...
suppose a police detective is about to administer a polygraph
(lie detector) test on an "individual of interest" . when a
polygraph is administered to an individual who is lying, the chance
that the test detects that the individual is lying is 90%.
additionally, when polygraph test is administered to an individual
who is telling the truth, the chance that the test indicates that
the individual is not lying is 84%. finally, the police detective
knows that "individuals of interest"...
A new? lie-detector test has been devised and must be tested before it is put into...
A new? lie-detector test has been devised and must be tested
before it is put into use. Three hundred people are selected at?
random, and each person draws and keeps a card from a box of 300
cards. Half the cards instruct the person to lie and the others
instruct the person to tell the truth. Of those who? lied, 70?%
fail the new? lie-detector test? (that is the test indicated?
lying). Of those who told the? truth, 5?% failed...
A new lie-detector test has been devised and must be tested before it is put into...
A new lie-detector test has been devised and must be tested
before it is put into use. 200 people are selected at random, and
each person draws and keeps a card from a box of 200 cards. Half
the cards instruct the person to lie and the others instruct the
person to tell the truth. Of those who lied, 85% fail the new
lie-detector test (that is the test indicated lying). Of those
who told the truth, 5% failed the...
Design a sequence detector to detect either 01 or 10 sequences. Include a reset state. Show...
Design a sequence detector to detect either 01 or 10 sequences.
Include a reset state. Show the state transition diagram,
state table, K-maps, and complete circuit.
A survey taken several years ago found that the average time a person spent reading the...
A survey taken several years ago found that the average time a
person spent reading the local newspaper was 10.8 minutes. The
standard deviation of the population was 3 minutes. To see whether
the average time had changed since the newspaper’s format had
changed, the editor surveyed 36 individuals. The average time that
these 36 people spent reading the newspaper was 11.2 minutes. At
= 0.05 , is the average time an individual spends reading the
newspaper still 10.8?...
The table below includes results from polygraph (lie detector) experiments conducted by researchers. In each case,...
The table below includes results from polygraph (lie detector)
experiments conducted by researchers. In each case, it was known if
the subjected lied or did not lie, so the table indicates when the
polygraph test was correct. Use a 0.05 significance level to test
the claim that whether a subject lies is independent of the
polygraph test indication. Do the results suggest that polygraphs
are effective in distinguishing between truth and lies?
. Determine the null and alternative hypotheses.
A....
The table below includes results from polygraph (lie detector) experiments conducted by researchers. In each case,...
The table below includes results from polygraph (lie detector)
experiments conducted by researchers. In each case, it was known
if the subjected lied or did not lie, so the table indicates when
the polygraph test was correct. Use a 0.05 significance level to
test the claim that whether a subject lies is independent of the
polygraph test indication. Do the results suggest that polygraphs
are effective in distinguishing between truth and lies?
Did the Subject
Actually Lie?
No (Did Not...
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