Question: Estimate the probability that a person who knows 60% of the material gets a grade strictly between 50 and 70 in the test of Exercise.
Exercise: Compute the variance for the number of right answers when we answer one question with probability .8 of getting the right answer (note that the number of right answers is either 0 or 1, but the expected value need not be). Compute the variance for the number of right answers when we answer 5 questions with probability .8 of getting the right answer. Do you see a relationship?