Using the Binomial Distribution Assume that two students must take a ten question, True or False...

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?

Solutions

Expert Solution

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.

orchestra answered 1 year ago

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