Suppose an instructor gave four (4) multiple-choice questions on the final and a

Question

Suppose an instructor gave four (4) multiple-choice questions on the final and after giving the questions computed the probabilities of the number of problems correct for the students (which are given below).

# of Correct MC

0

1

2

3

4

Probability

0.08

0.18

0.26

0.35

0.13

What is the mean number of correct multiple-choice problems the instructor should expect to see?

Let us continue working with multiple-choice problems, but let us say instead that the instructor has ten (10) multiple-choice problems.

What are the four requirements for an experiment to be a binomial experiment?

Do the ten multiple-choice questions satisfy those requirements? Explain your answer.

What is the probability of obtaining exactly 8 correct answers?

What is the probability of obtaining at least 8 correct answers?

What is the probability of obtaining at most 7 correct answers?

# of Correct MC

0

1

2

3

4

Probability

0.08

0.18

0.26

0.35

0.13

Explanation / Answer

Mean=0*0.08+1*0.18+2*0.26+3*0.35+4*0.13=2.27

The four requirements are

1-There should be fixed number of finite trials

2-Trials should be independent

3-Each trial has only two possible outcomes

4-Theprobabaility of success(desired outcome) should be constant from trial to trial

The 10MCQ satisfies the above requirements as there are fixed 10 trials each with two outcome of correct/incorrect answer which is constant p=1/4=0.25 from trial to trial. Also, 10 questions are independent.

So, X follows Binomial with n=10 andp=0.25

Hence,P(X=8)= 0.0004 using excel function =BINOMDIST(8,10,0.25,FALSE)

P(X>=8)=1-P(X<=7)= 0.0004 using excel function =1-BINOMDIST(7,10,0.25,TRUE)

P(X<=7)= 0.9996 using excel function =BINOMDIST(7,10,0.25,TRUE)

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