Prompt : A friend tells you he only needs a 25% on the final exam to pass his st

Question

Prompt:

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 what you have learned about the binomial distribution to answer the following questions.

Response parameters:

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

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

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.

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

Sample size n will make difference here since for binomial distribution

P(X=x) = nCr*P^x*(1-P)^(n-x)

where P= Prob of success

n= sample size,

x= no. of total trials

So, if my friend has to pass he/she has to score at least 25%.

If there are total 20 questions then he has to score at least 20*.25= 5 questions correct

P(X=5)= 0.2 &

P(X<5)= =BINOM.DIST(5,20,0.25,TRUE)= 0.617

Thus, P(X>=5)= 1-P(X<5) = 0.38 = 38%

If n=100, then

Thus, P(X>=5)= 1-P(X<5) = 1-0.00 = 1 =100% almost
means if questions increases, his prob to pass will increase.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

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