Guessing Answers The final exam in a sociology course consists of 100 multiple-c
ID: 2954021 • Letter: G
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Guessing Answers The final exam in a sociology course consists of 100 multiple-choice questions. Each question has 5 possible answers, and only 1of them is correct. An unprepared student makes random guesses forall the answers. a) Find the mean and standard deviation for the numberof correct answers for such students. b) Would it be unusual for a student to pass the exam byguessing and getting at least 60 correct answers? Why or whynot? Guessing Answers The final exam in a sociology course consists of 100 multiple-choice questions. Each question has 5 possible answers, and only 1of them is correct. An unprepared student makes random guesses forall the answers. a) Find the mean and standard deviation for the numberof correct answers for such students. b) Would it be unusual for a student to pass the exam byguessing and getting at least 60 correct answers? Why or whynot?Explanation / Answer
Therefore, the mean is just n (number of trials) * p(probability of success on a single trial) = 100 * .20 =20.
The standard deviation is sqrt[np(1-p)]. That issqrt(100 * .2 * .8) = sqrt(16) = 4
It would be unusual for a student to pass by guessing andgetting at least 60 correct answers because 60 is 10 standarddeviations higher than the mean. (60-20)/4 = 10 (z-score). If we look at a z-table for a normal distribution, almost 99percent of scores fall within 3 standard deviations higher or lowerthan the mean. 10 standard deviations is near statisticallyimpossible.
Therefore, it is very unusual for a student to pass the examby guessing and getting at least 60 correct answers.
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