Aldrich Ames is a convicted traitor who leaked American secrets to a foreign power. Yet Ames took routine lie detector tests and each time passed them. How can this be done? Recognizing control questions, employing unusual breathing patterns, biting one’s tongue at the right time, pressing one’s toes hard to the floor, and counting backward by 7s are countermeasures that are difficult to detect but can change the results of a polygraph examination (Source: Lies! Lies!! Lies!!! The Psychology of Deceit, by C. V. Ford, professor of psychiatry, University of Alabama). In fact, it is reported in Ford’s book that after only 20 minutes of instruction by “Buzz” Fay (a prison inmate), 85% of those trained were able to pass the polygraph examination even when guilty of a crime. Suppose that a random sample of nine students (in a psychology laboratory) are told a “secret” and then given instructions on how to pass the polygraph examination without revealing their knowledge of the secret. What is the probability that:
(a) All the students are able to pass the polygraph examination?
(b) More than half the students are able to pass the polygraph examination?
(c) No more than four of the students are able to pass the polygraph examination?
(d) All the students fail the polygraph examination?
The binomial distribution will be used. Answers may vary slightly depending on whether the binomial distribution formula, the binomial distribution table, or distribution results from a calculator or computer are used. Please answer the following questions and then complete the problem: What makes up a trial? What is a success? What is a failure? What are the values of n, p, and q?