The Modeling of Multiple-Choice Questions Using Binomial Distribution

Abstract

One weakness of multiple-choice tests is that it gives a chance for test takers to correctly answer the question without knowing for sure that the selected response is the right one. A good admission test is a multiple-choice test combination that minimizes the probability of answering the question correctly by randomly guessing it. In this way, the multiple-choice test will be able to serve its function as a performance differential or for each test taker. In this article, a mathematical model that can be used to see the risk of admitting low-performing students for passing the admission selection using multiple-choice tests will be built. The model is made based on a binomial distribution combination. The model can be designed to choose the sets of multiple-choice tests that minimize the probability of admitting low-performing participants. The research methodology is to review the literature. In this article, we analyze two examples of applications. The illustration in an example of application 1 gives a result that setting the passing grade at 50 allows only 1 low performing participant out of 1,000,000 participants to pass the test for answering the questions correctly merely by randomly guessing it. Test II in an example of application 2 is more homogeneous and sharper in measuring the participants’ performance.