Suppose That Julie And Kevin Are Both Very Skilled Basketball Players And Decide To Compete In Some Basketball Shooting 1 (56.43 KiB) Viewed 62 times
Suppose That Julie And Kevin Are Both Very Skilled Basketball Players And Decide To Compete In Some Basketball Shooting 2 (56.43 KiB) Viewed 62 times
Suppose that Julie and Kevin are both very skilled basketball players and decide to compete in some basketball shooting games. a) (26 pts.) Julie and Kevin start with a free throw contest, in which each player stands behind the free-throw line and attempts to shoot a basketball through the hoop. The contest consists of 20 attempts for each player, with the winner being the player who successfully made more shots than the other player; the contest ends in a tie if the players score the same amount of points. Suppose that Julie and Kevin are equally matched in shooting ability, such that they both make 70% of their attempts. i. Compute the probability that Kevin makes at least 15 shots out of 20 attempts. State any assumptions required to make this calculation. ii. Simulate 10,000 replicates of the described contest to estimate the probability of Julie winning, the probability of Kevin winning, and the probability of the contest ending in a tie. Briefly describe the logic of the simulation and clearly comment your code. iii. Let J be the number of shots Julie makes, K the number of shots Kevin makes, and D the difference in number of shots made (where D=J-K). Does D follow a binomial distribution? Explain your reasoning.
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