Madam Helga claims to be psychic. A national TV talk personality plans to test her in a live TV broadcast. The process will entail asking Madam Helga a series of 20 independent questions with yes/no answers. The questions would be of the nature that she could not have any way of knowing the answer from prior knowledge. She will be considered psychic if she correctly answers more than a specified number (called the cut-off) of the questions. The cut-off must be set so that the chance of guessing that number or more is no greater than 5 percent. The cut-off value should be:

Question

Quizplus · Accepted Answer

For a series of 20 independent yes/no questions, each with a 50% chance of being answered correctly by guessing, the situation can be modeled using a binomial distribution with parameters n = 20 (number of trials) and p = 0.5 (probability of success on each trial). The cut-off value is the smallest number of correct answers for which the cumulative probability of guessing that many or more correctly is less than or equal to 5%. Using binomial distribution tables or a calculator, we find that the cut-off where the cumulative probability first drops to 5% or lower is at 15 correct answers out of 20. Therefore, to have a less than or equal to 5% chance of guessing correctly by chance, Madam Helga must answer more than 14 questions correctly, making the correct cut-off 14.

Madam Helga Claims to Be Psychic