Polygraph lie-detector machines are commonly used in criminal investigations. The device measures nervous excitement, operating on the idea that if a person is telling the truth they will remain calm. The American Polygraph Association claims that polygraphs accurately identify liars 90% of the time. In other words, if a person lied the test results will be positive 90% of the time. Although the polygraph test is good at identifying liars, there is a 50% chance that the polygraph test will say a truthful person is lying. A police force wants to predict the accuracy of lie-detector tests for 1,000 suspected criminals. Assume that 700 per 1,000 suspected criminals tell the truth during polygraph tests. Lie Truth Row Totals Test result: negative P Test result: postive Q Column Totals 1,000 Barber, N. (2013). Do Lie Detectors Work? Psychology Today . What is the probability that a person is telling the truth given that the lie detector test has a positive result? Group of answer choices 350 out of 700= 0.50 350 out of 1,000 = 0.35 350 out of 620 = 0.56 350 out of 380 = 0.92

0.5645

This means a person telling the truth is flagged as a liar 56.45% of the time. No, Polygraph lie detector machines do not work as this is too much a statistic for the innocent.

Step-by-step explanation:

Liars are identified 90% of the time.

Truth tellers are identified as truth tellers 50% of the time.

Out of 1000 Criminals, 700 criminals are telling the truth

Meaning 300 criminals are lying

Of the 700 truth tellers, the machine gets

it right 50% of the time

Meaning 350 positive results and 350 negative results.

Of the 300 liars, the machine gives a positive result 90% of the time.

Positive result = 0.9 × 300 = 270

Negative result = 0.1 × 300 = 30

The table of results is presented in the second attached image

The probability that a person is telling the truth given that the lie detector test has a positive result

The lie detector test gives a positive result 620 times

A person is telling the truth and the result gives a positive result 350 times.

Probability that a person is telling the truth given that the result is positive = (probability that a person is telling the truth and the machine gives a positive result)/(total number of positive results that the machine gives) = (350/620) = 0.5645

describing distributions is one of the key skills you’ll need to earn a high score on the ap statistics exam. if you need proof of this, just flip through some past exam questions, which can be found at the collegeboard website. you’ll notice that the first free response question is almost always a question requiring you to look at a graph and describe it.

step-by-step explanation: just trying to get points sorry : (