# Binomial distribution example problems and answers

This activity is appropriate for a introductory level business statistics course. It is appropriate for use in any size class. It can be used either to introduce the concepts of the binomial distribution, or to assess students' understanding after the binomial distribution has been discussed. If the problem is done in class it will take about minutes to complete. You are watching an episode of Law and Order. The plot for this episode includes a scientist that was trying to communicate with patients in a persistent vegetative state.

She put two signs in front of the patients. The sign on the right side of the patient read 'Yes. In the show there is a disagreement over whether or not the scientist was actually communicating with these patients, or if she was simply recording random eye movements in these patients.

The scientist claimed the percent of correct responses she got showed she was able to communicate with these patients. What percent of correct responses do you believe she should have gotten in order to claim she was able to communicate with the patients? This activity can be done in class individually or in small groups. It can also be assigned as a homework problem or as an exam question. Students need to have some familiarity with the binomial probability distribution to successfully complete the problem.

If your students are new to context-rich problems, you may want to include prompts to help students, such as 'What probability distribution is best suited to a situation like this one? You should expect to see students attempting to apply a wide variety of probability rules.

It can also be assigned as a homework problem or as an exam question. Students need to have some familiarity with the binomial probability distribution to successfully complete the problem. If your students are new to context-rich problems, you may want to include prompts to help students, such as 'What probability distribution is best suited to a situation like this one? You should expect to see students attempting to apply a wide variety of probability rules.

Class discussion can focus on what types of questions are answered with the probability rules they have applied and how these questions differ from the one posed. The purpose of the assessment will determine whether or not you need a rubric. If the problem will be graded, it may be helpful to give the students a rubric such as: All statistical reasoning in the answer is correct.

All relevant calculations are included. May have minor mistakes, such as a minor error in a calculation. Statistical reasoning in the answer is correct, but the answer contains minor mistakes such as calculation errors.

Contains significant errors in the statistical reasoning, such as missing steps in the problem solving process, or several significant errors in calculations. Very little of the statistical reasoning is correct and relevant to the problem. None of the economic content is relevant to the question.

Teaching and Learning Economics Starting Point: Why Teach with Context-Rich Problems?