Most binomial probability calculations required in these exercises can be done by using Table C or the Normal approximation. Your instructor may request that you use the binomial probability formula or software. In exercises requiring the Normal approximation, you should use the continuity correction if you studied that topic.

Question 5.31

5.31 Shooting free throws.

Since the mid-1960s, the overall free throw percent at all college levels, for both men and women, has remained pretty consistent. For men, players have been successful on roughly 69% of these free throws, with the season percent never falling below 67% or above 70%.10 Assume that 300,000 free throws will be attempted in the upcoming season.

  1. What are the mean and standard deviation of if the population proportion is ?
  2. Using the 68–95–99.7 rule, we expect to fall between what two percents about 95% of the time?
  3. Given the width of the interval in part (b) and the range of season percents, do you think that it is reasonable to assume that the population proportion has been the same over the last 50 seasons? Explain your answer.

5.31

(a) . (b) Between 0.6883 and 0.6917. (c) No, the actual percentages are much more variable than the interval, suggesting that the percent has changed from season to season.