Chapter 5.7, Problem 11E

On January 1 of a given year, a college basketball player will shoot free throws in practice until he makes ten of them. He will repeat this random experiment on each day of January that year. Let $X_i$ denote the number of free throw attempts it takes the basketball player to make ten free throws on the ith day of January (1 = 1,2,...,31). Treating $X_1,X_2,\mathrm{...},X_{31}$ as a random sample from a negative binomial distribution, and assuming that the probability of success (i.e.. the probability that he makes a free throw in one attempt) is equal to $\frac{2}{3}$ every day, approximate the probability that the total number of free throws attempted by the basketball player is less than or equal to 500.