On average, 2 percent of all persons who are given a breathalyzer test by the state police pass the test (blood alcohol under .08 percent). Suppose that 500 breathalyzer tests are given. (a) What is the expected number who pass the test? (b) What is the approximate Poisson probability that 5 or fewer will pass the test?
The probability of an incorrect call by an NFL referee is .025 (e.g., calling a pass complete, but the decision reversed on instant replays). In a certain game, there are 150 plays. (a) What is the probability of at least 4 incorrect calls by the referees? (b) Justify any assumptions that you made.