Question

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 answers to different questions are independent. Jodi is a good student for whom p = 0.75.

(a) Use the Normal approximation to find the probability that Jodi scores 70% or lower on a 100-question test. (Round your answer to four decimal places.)

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(b) If the test contains 250 questions, what is the probability that Jodi will score 70% or lower? (Use the normal approximation. Round your answer to four decimal places.)
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(c) How many questions must the test contain in order to reduce the standard deviation of Jodi's proportion of correct answers to half its value for a 100-item test?
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(d) Laura is a weaker student for whom p = 0.7. Does the answer you gave in (c) for standard deviation of Jodi's score apply to Laura's standard deviation also? choose one A or B

A.Yes, the smaller p for Laura has no effect on the relationship between the number of questions and the standard deviation.

B.No, the smaller p for Laura alters the relationship between the number of questions and the standard deviation.    

Answer 1

A.Yes, the smaller p for Laura has no effect on the relationship between the number of questions and the standard deviation.