Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p...

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Here is a simple probability model for multiple-choice tests.Suppose that each student has probability p of correctlyanswering a question chosen at random from a universe of possiblequestions. (A strong student has a higher p than a weakstudent.) The correctness of answers to different questions areindependent. Jodi is a good student for whom p = 0.82.
(a) Use the Normal approximation to find the probability thatJodi scores 77% or lower on a 100-question test. (Round your answerto four decimal places.)

(b) If the test contains 250 questions, what is the probabilitythat Jodi will score 77% or lower? (Use the normal approximation.Round your answer to four decimal places.)

(c) How many questions must the test contain in order to reduce thestandard deviation of Jodi's proportion of correct answers to halfits value for a 100-item test?
questions

(d) Laura is a weaker student for whom p = 0.77. Does theanswer you gave in (c) for standard deviation of Jodi's score applyto Laura's standard deviation also?
Yes, the smaller p for Laura has no effect on therelationship between the number of questions and the standarddeviation.No, the smaller p for Laura alters therelationship between the number of questions and the standarddeviation

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4.4 Ratings (655 Votes)

a As we known that by central limit theorem binomialdistribution is tends to normal approximation as n is largeHere n 100 p 082 np10 So we use the See Answer

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