What is the probability distribution of x this test

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Unformatted text preview: oices for each of the 25 questions. What is the probability distribution of X ? This test, like many multiple-choice tests, is scored using a penalty for guessing. The test score is determined by awarding 1 point for each question answered correctly, deducting 0.25 point for each question answered incorrectly, and ignoring any question that is omitted. That is, the test score is calculated using the following formula. Score = (1 ¥ number of correct answers) – (0.25 ¥ number of incorrect answers) + (0 ¥ number of omits) For example, the score for a student who answers 17 questions correctly, answers 3 questions incorrectly, and omits 5 questions is Score = (1 ¥ 17) - (0.25 ¥ 3) + (0 ¥ 5) = 16.25. (b) Suppose a student knows the correct answers for 18 questions, answers those 18 questions correctly, and chooses randomly from the 5 choices for each of the other 7 questions. Show that the expected value of the student’s score is 18 when using the scoring formula above. (c) A score of at least 20 is needed to pass the test. Suppose a student knows the correct answers for 18 questions, answers those 18 questions correctly, and chooses randomly from the 5 choices for each of the other 7 questions. What is the probability that the student will pass the test? © 2010 The College Board. Visit the College Board on the Web: www.collegeboard.com. GO ON TO THE NEXT PAGE. -7- 2010 AP® STATISTICS FREE-RESPONSE QUESTIONS (Form B) 4. A husband and wife, Mike and Lori, share a digital music player that has a feature that randomly selects which song to play. A total of 2,384 songs were loaded onto the player, some by Mike and the rest by Lori. Suppose that when the player was in the random-selection mode, 13 of the first 50 songs selected were songs loaded by Lori. (a) Construct and interpret a 90 percent confidence interval for the proportion of songs on the player that were loaded by Lori. (b) Mike and Lori are unsure about whether the player samples the songs with replacement or without re...
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