Question

Statistical Reasoning in sports

15. Suppose that a basketball player has the ABILITY to make 75% of her free- throws. The following dotplots show the results of 100 sets of 50 free-throw attempts and 100 sets of 200 free-throw attempts. COOOOOOOOO 000000OOOOOOO 00000000000000000000 0000000000 0000000000000000 00000000000 000000 000 o 000 00 • 000 000 000 • 000 00000000000000 0 00 00 00 00 00 00 00 00 00 000000000000 00 65 70 75 80 85 68 70 72 74 76 78 80 82 84 Simulated Percentage of Made Free-Throws Simulated Percentage of Made Free-Throws (a) What value is in the middle of each distribution? Explain why this is not surprising. (b) Which distribution is the one showing the results of 50 free-throws and which is the one showing the results of 200 free-throws? Explain.

Answer 1

(a) 76 is in the middle of each distribution. It is not surprising because the player is able to make 75% of her free throws. Hence 76% in the middle of the simulation is not surprising.

(b) The first distribution is showing 50 free-throw attempts and the second distribution is showing 200 free-throw attempts because the variation in 50 free-throw attempts is larger than the variation in 200 free-throw attempts. And this was expected because as the number of attempts will increase the variation is expected to decrease.

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