document.write( "Question 1206492: 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 backwards by 7 are countermeasures that are difficult to detect but can change the results of a polygraph examination†. In fact, it is reported in Professor 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 five 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 no more than half of the students are able to pass the polygraph examination? \n" ); document.write( "

Algebra.Com's Answer #844497 by Shin123(626) $\"\"$ $\"About$

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No more than half of the students means 0, 1, or 2 students passed. This is a binomial distribution. The probability is
\n" ); document.write( " $\"0.15%5E5%2B5%2A0.85%2A0.15%5E4%2B10%2A0.85%5E2%2A0.15%5E3\"$ .
\n" ); document.write( "The $\"0.15%5E5\"$ term represents the probability that none of the students passed. Since each student as a 85% pass rate, they have a 15% fail rate.
\n" ); document.write( "The $\"5%2A0.85%2A0.15%5E4\"$ term represents the probability that 1 student passed. The $\"0.85%2A0.15%5E4\"$ is the probability that 1 student passes and 4 fail, and it is multiplied by $\"5\"$ because there are 5 possible ways to pick a student that passes.
\n" ); document.write( "The final term $\"10%2A0.85%5E2%2A0.15%5E3\"$ is for 2 students passing. Again, the $\"0.85%5E2%2A0.15%5E3\"$ term is the probability that any 2 given students pass and the other 3 fail. There are $\"5C2=10\"$ ways to pick these 2 students.
\n" ); document.write( "Plugging this into a calculator, we get the probability as 0.0266 (rounded to 4 decimal places).
\n" ); document.write( "If you need more precision, plug it into a calculator yourself either online or on an actual calculator. \n" ); document.write( "

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