7. Passing by Guessing Binomial Distributions A quiz in a statistics course has

Question

7. Passing by Guessing Binomial Distributions A quiz in a statistics course has 12 multiple-choice questions, each with 4 possible answers. Alena has not studied for the quiz and has no idea of the correct answers, so she decides to guess at a random answer for each question a. State specifically how this problem satisfies each of the three conditions for a binomial distribution (Refer to your notes for these conditions.) State the value for n and p. Find the probability she answers 7 questions correctly. Give this probability as a b. c. percent rounded to two decimal places

Explanation / Answer

n = 12

p = Probability of marking a correct answer = 1/4 = 0.25

q = Probability of marking a wrong answer = 3/4 = 0.75

a)

Limited trails, here n=12

Independent trails; all answers are independent of each other

Probability of success is indicated by p and failure by 1-p as there are only two possible outcomes- right/wrong

b)

n = 12

p = 0.25

c)

P(X=7) = C(12,7)*(0.25)^7*(0.75)^5 = 0.0114

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