A National Basketball Association player has made 80% of his free-throw attempts in the past. This season he takes 150 free throws. Basketball free throws are always attempted from 15 feet away with no interference from other players.
Is it reasonable to expect that binomial distribution will at least approximately explain the number of successful free-throws? Discuss your answer.
A. The number of successes doesn't have binomial distribution because the throws are not independent.
B. The number of successes doesn't have binomial distribution. The probability of success differs wildly for each throw.
C. Here, the number of successes is more likely to be at least approximately binomial distributed. There is a fixed number of independent throws - 150, and it is reasonable to assume that all have approximately the same probability of success, 0.8.
D. The number of successes doesn't have a binomial distribution because the number of observations is not fixed.