Here is a simple probability model for multiplechoice 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.

4. 0/3 points | Previous Answers My Notes Reference: Chapter 5.1 Summary 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 = 0.84. Use 4 decimal places (a) Use the normal approximation to find the probability that Jodi scores 79% or lower on a 100-question test. (b) If the test contains 250 questions, what is the probability that Jodi will score 79% or lower? 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? Enter a number

Solution

p=0.84 for jody

n=100

We know binomial becomes normal when n becomes large with mean

= np = 84 and std dev = rt npq = 3.667

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X the score of Jody is normal with mean 84 and sd 3.667

P(X<=79) = P(Z<= -1.36) = 0.0869

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If n =250, mean = 250(0.84) = 210 and sd = 5.80

P(x<=79%) = P(x<=197.5)

z= -12.5/5.80 = -2.16

P(X<=79%) = 0.0154

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sd = 1.838

npq = 1.838²= 3.378

n = 3.378/0.84(0.16) =25.13

n can be 26.