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12. (10 points) A college basketball player makes 90% of his free throws. Assuming free-throw attempts...

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12. (10 points) A college basketball player makes 90% of his free throws. Assuming free-throw attempts...

12. (10 points) A college basketball player makes 90% of his free throws. Assuming free-throw attempts are independent. Over the course of the season, he will attempt 100 free throws. a) Use binomial distribution to find the exact probability that the number of free throws he makes is between 85 and 95, inclusive. b) Check the conditions for using the normal appreciation to the binomial distribution c) Use normal approximation to estimate the probability that the number of free throws he makes is between 85 and 95, inclusive. Please do not apply the continuity correction in this part. d) Use normal approximation to estimate the probability that the number of free throws he makes is between 85 and 95, inclusive. Please apply the continuity correction in this part. e) Compare the two approximations (with and without using the continuity correction). Which one is closer to the exact probability in a)?

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