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What is normal?

 
Marc Peabody
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The MD has a thread titledHow normal are you? that has a link to a quiz that tells you how "normal" you are.

The quiz has twenty questions and each question has two choices. Answering a question correctly adds 5% to your total score.

The test results do not reveal which questions were right or wrong. Your only result from each test submission is a total percentage.

Problem: I want to know what the test's author thinks is "normal" by the fewest number of test submissions possible. I can not assume that the author is normal or abnormal.

I am allowed to leave questions blank and those questions count as not-normal responses.

Is there a better answer than 20? Why?
 
Adam Vinueza
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I'm just thinking off the top of my head here, but my sense is that the answer is No. Consider a quiz with only two questions; for simplicity, suppose the answers are limited to Yes and No. The best one can do here is guess, so we might as well answer Yes to both questions, and see what percentage results. The worst case is 50%, in which case one has to use another guess to find out which of the two has a Yes answer. That is, it takes a guess to determine whether a particular question has a particular answer, after the initial guess. In the n-question case, changing more than one unknown doesn't help in the worst case, as it might yield no information (if an even number of unknowns are changed), or information that requires no fewer guesses than changing one (as when there is a net gain of only one right answer). So it looks to me like 20 guesses for 20 questions is optimal.
 
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