EXAMPLE 5.7 Free Throws

Jessica is a basketball player who makes 75% of her free throws over the course of a season. In a key game, Jessica shoots 12 free throws and misses five of them. The fans think that she failed because she was nervous. Is it unusual for Jessica to perform this poorly?

To answer this question, assume that free throws are independent with probability 0.75 of a success on each shot. (Many studies of long sequences of basketball free throws have found essentially no evidence that they are dependent, so this is a reasonable assumption.)⁴ Because the probability of making a free throw is greater than 0.5, we count misses in order to use Table C. The probability of a miss is , or 0.25. The number of misses in 12 attempts has the binomial distribution with and .

We want the probability of missing five or more. This is

250

Jessica will miss five or more out of 12 free throws about 16% of the time. While below her average level, her performance in this game was well within the range of the usual chance variation in her shooting.