On a 20 question multiple choice exam, each question has 5 answer choices. An un

Question

On a 20 question multiple choice exam, each question has 5 answer choices. An unprepared student guesses the answer to each question.

a. What is the probability that the student gets exactly 4 questions correct?

b. What is the probability that the student gets more than 4 questions correct?

c. What is the expected number of questions that the student will answer correctly?

d. What is the standard deviation of the number of questions the student will answer correctly?

e. Suppose 60% of the questions must be answered correctly in order to pass the exam. A student claims to have passed the exam by guessing the answer to each question. Do you believe the student? Why or why not? Show work to support your answer.

Explanation / Answer

Result:

On a 20 question multiple choice exam, each question has 5 answer choices. An unprepared student guesses the answer to each question.

a. What is the probability that the student gets exactly 4 questions correct?

n=20, p=0.2

Binomial distribution used.

P(X=x) = (nCx) px (1-p)n-x

P( x=4) = 0.2182

b. What is the probability that the student gets more than 4 questions correct?

P( x>4) = 0.3704

c. What is the expected number of questions that the student will answer correctly?

Expectation = np = 20*0.20 = 4

d. What is the standard deviation of the number of questions the student will answer correctly?

Variance = np(1 - p) = 3.2

Standard deviation = 1.7889

e. Suppose 60% of the questions must be answered correctly in order to pass the exam. A student claims to have passed the exam by guessing the answer to each question. Do you believe the student? Why or why not? Show work to support your answer.

60% of the questions = 12

12 questions be answered correctly in order to pass the exam

P( x 12 ) = 0.00001

This probability is very small.

We are not believing the claim that pass the exam by guessing the answer to each question.

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