Problem: LeBron's free throws. The basketball player LeBron James makes about three-quarters of his free throws over an entire season. Use the Probability applet or statistical software to simulate 100 free throws shot by a player who has probability 0.75 of making each shot. (In most software, the key phrase to look for is "Bernoulli trials." This is the technical term for independent trials with Yes/No outcomes. Our outcomes here are "Hit" and "Miss.")
Required:
(i) What percent of the 100 shots did he hit?
(ii) Examine the sequence of hits and misses. How long was the longest run of shots made? Of shots missed? (Sequences of random outcomes often show runs longer than our intuition thinks likely.)