A university claims that at least 80% of its basketball players get degrees. To see if there is evidence to the contrary, an investigation examines the fate of 20 players who entered the program over a period of several years that ended six years ago. Of these players, 11 graduated and the remaining nine are no longer in school, if the university's claim is true, the number of players who graduate among the 20 should have the binomial distribution with n 20 and p at least equal to 0.8. (a) Find the mean number of graduates out of 20 players if 80% of players graduate (b) Find the standard deviations of the count Xi 80% of players graduate (c) Suppose now that the 20 players came from a population of which p = 0.9 graduated. What is the standard deviation of the count of graduates? If p *0.99, What is the standard deviation? What does your work show about the behavior of the standard deviation of a binomial distribution as the probability of success gots closer to 1