Suppose an instructor gave four (4) multiple-choice questions on the final and a
ID: 3234336 • Letter: S
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)