Statistics : A friend tells you he only needs a 25% on the final exam to pass hi

Question

Statistics:

A friend tells you he only needs a 25% on the final exam to pass his statistics class, and since the exams are always multiple choice with four possible answers he can randomly guess at the answers and still get 25%. Use binomial distribution to answer the following questions.

Questions to answer:

1. What do you think about your friend’s idea? Why?

2. What do you think his chances of getting at least 25% on the exam are?

3. Do the number of questions on the exam make a difference? If it does, should your friend hope for a 20 question exam or a 100 question exam.

4. Create a table of Binary probabilities with p = 0.25 and n = number of questions on the exam.

5. Also, don’t confuse the probability of getting exactly 25% of the questions correct and getting at least 25% of the questions correct

Explanation / Answer

1)Mean=np=100*0.25=25

Variance=npq=100*0.25*0.75=18.75

SD=sqrt(18.75)=4.33

Hence the friends idea is decent enough but he will have a risk of not getting pass also.

2)P(X>25)=P(Z>0)=0.5

3)More the number of questions,more is the chance of tending towards the mean 25%.Hence he should hope for a 100 question exam.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.