Final answer:
Alex will use a TI-83 or TI-84 calculator to determine the probability of no false positives in a sample of 10 individuals given a 9.1% chance of a false positive per test. Using binompdf(10, 0.909, 10), he will find the reliability of the polygraph tests. If the probability of no false positives is greater than 95%, he can conclude the tests are reliable.
Step-by-step explanation:
Analysis of Polygraph Test Reliability
Alex is assessing the reliability of polygraph tests and is using a TI-83 or TI-84 calculator to calculate the probability of no false positives in a random sample of 10 individuals. Given that the probability of a single false positive is 9.1%, we need to determine the probability of getting no false positives over the 10 tests to see if this probability is above 95%.
Firstly, let's assume each test is independent. The probability of a true statement being recorded as true (no false positive) in each test is 1 - 0.091 (or 90.9%). We can use the binomial distribution with parameters n = 10 (number of trials) and p = 0.909 (probability of success on a single trial), to find the probability of 10 successes (no false positives across all tests).
To calculate this using a TI-83 or TI-84 calculator:
- Go to the binompdf function by pressing 2nd then vars (to get to the DISTR menu).
- Scroll down to binompdf and select it.
- Enter the parameters: binompdf(10, 0.909, 10).
- Press ENTER to get the result.
The calculator will provide the probability of 10 successes out of 10 trials, which is the probability of having no false positives in all tests. If this probability is higher than 95%, Alex can conclude that the polygraph tests are reliable according to his criteria.