A multiple-choice exam consists of 50 questions. Each

Chapter 0, Problem 7.42

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A multiple-choice exam consists of 50 questions. Each question has five choices, of which only one is correct. Suppose that the total score on the exam is computed as where x1 number of correct responses and x2 number of incorrect responses. (Calculating a total score by y x1 1 4 x2 subtracting a term based on the number of incorrect responses is known as a correction for guessing and is designed to discourage test takers from choosing answers at random.) a. It can be shown that if a totally unprepared student answers all 50 questions by just selecting one of the five answers at random, then and . What is the mean value of the total score, y? Does this surprise you? Explain. b. Explain why it is unreasonable to use the formulas given in this section to compute the variance or standard deviation of y.

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