A teacher is trying to decide whether to have 4 or 5 choices

A teacher is trying to decide whether to have 4 or 5 choices per question on her multiple choice test. She wants to prevent students who just guess from scoring well on the test. She wants the test to be 5 questions. Assume X has a binomial distribution and let X = number of correctly guessed answers. Use the following information on the remaining problems.

Write the following in terms of x in part A and in part B determine the probability 26. No more than 2 questions are guessed correctly if each question has 4 choices. A. X = ______________ B. Probability = ____________ 27. No more than 2 are guessed correctly if each question has 5 choices. A. X = ______________ B. Probability = ____________

Solution

No of questions 5

Case I: 4 multiple choices

p = prob for right answer by guessing = 0.25

26) P(X<=2)=0.8964

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Case 2: 5 multiple choices

p = 0.20

27) P(X<=2) =0.9421