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Multiple-choice tests. Here is a simple probability model
Chapter , Problem 5.71(choose chapter or problem)
Multiple-choice tests. Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of an answer to a question is independent of the correctness of answers to other questions. Jodi is a good student for whom p 0.88. (a) Use the Normal approximation to find the probability that Jodi scores 85% or lower on a 100-question test. (b) If the test contains 250 questions, what is the probability that Jodi will score 85% or lower? (c) How many questions must the test contain in order to reduce the standard deviation of Jodis proportion of correct answers to half its value for a 100-item test? (d) Laura is a weaker student for whom p 0.72. Does the answer you gave in part (c) for the standard deviation of Jodis score apply to Lauras standard deviation also? 5
Questions & Answers
QUESTION:
Multiple-choice tests. Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of an answer to a question is independent of the correctness of answers to other questions. Jodi is a good student for whom p 0.88. (a) Use the Normal approximation to find the probability that Jodi scores 85% or lower on a 100-question test. (b) If the test contains 250 questions, what is the probability that Jodi will score 85% or lower? (c) How many questions must the test contain in order to reduce the standard deviation of Jodis proportion of correct answers to half its value for a 100-item test? (d) Laura is a weaker student for whom p 0.72. Does the answer you gave in part (c) for the standard deviation of Jodis score apply to Lauras standard deviation also? 5
ANSWER:a) From the normal approximation, we can calculate the probability of achieving 85% or lower on a 100-question test as 0.067. b) For a 250-question test, the probability of scoring 85% or lower is 0.00