Question

Using the Binomial Distribution

Assume that two students must take a ten question, True or False quiz. Student 1 has not studied at all and guesses randomly on each question. Student 2 has studied hard and has a 95% chance of answering any particular question correctly.

For each student, calculate the probability of passing (getting 7 or more correct answers) and the probability of “acing” (getting 9 or 10 correct answers) the quiz.

What do your calculated probabilities say about the amount of preparation students do and their probability of doing well on the quiz?

Answer 1

For each student, calculate the probability of passing (getting 7 or more correct answers)

The probability of passing for student 1 is:

We can use the excel below function to answer:

=1-BINOMDIST(6,10,0.5,TRUE)=0.1719

The probability of passing for student 2 is:

We can use the excel below function to answer:

=1-BINOMDIST(6,10,0.95,TRUE)=0.9990

Find the probability of “acing” (getting 9 or 10 correct answers) the quiz.

The probability of acing for student 1 is:

We can use the excel below function to answer:

=1-BINOMDIST(8,10,0.5,TRUE)=0.0107

The probability of acing for student 2 is:

We can use the excel below function to answer:

=1-BINOMDIST(8,10,0.95,TRUE)=0.9139

What do your calculated probabilities say about the amount of preparation students do and their probability of doing well on the quiz?

Answer: From the above results, we clearly see the preparation of student and the probability of doing well on the quiz is positively correlation. That is, if a student prepares well for the test, there will be a higher probability of him/her doing well on the quiz and if a student does not prepare well for the test, there will be a least probability of him/her doing well on the quiz.