Two students taking a multiple choice exam with 20 questions and four choices fo

Question

Two students taking a multiple choice exam with 20 questions and four choices for each question have the same, incorrect answer on eight of the problems. The probability that student B guesses the same incorrect answer as student A on a particular question is 1/4. If the student is guessing, it is reasonable to assume guesses for different problems are independent. The instructor for the class suspects the students exchanged answers. The teacher decides to present a statistical argument to substantiate the accusation. A possible model for the number of incorrect questions that agree is a: normal distribution with = 8 and = .25. binomial distribution with n = 8 and p = .25. normal distribution with = 20 and = .40. binomial distribution with n = 20 and p = .40. Two students taking a multiple choice exam with 20 questions and four choices for each question have the same, incorrect answer on eight of the problems. The probability that student B guesses the same incorrect answer as student A on a particular question is 1/4. If the student is guessing, it is reasonable to assume guesses for different problems are independent. The instructor for the class suspects the students exchanged answers. The teacher decides to present a statistical argument to substantiate the accusation. A possible model for the number of incorrect questions that agree is a: normal distribution with = 8 and = .25. binomial distribution with n = 8 and p = .25. normal distribution with = 20 and = .40. binomial distribution with n = 20 and p = .40.

Explanation / Answer

The arguement that the two students cheated on a test can be proved by a hypothesis that both the students got the same answers incorrect.

So,

We reduce our sample to the number of incorrect answers i.e n = 8

Then, p = probability of success = both students choosing the same option = 0.25

Since. there can be only two possible outcomes of this propostion i.e choosing the same answer or not choosing the same answer, this can be handles via a binomial distribution model.

Hence,

option B is correct

Hope this helps.

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