1. A university claims that at least 75% of its basketball players get degrees. An investigation examines the fate of 25 players who entered the program over a period of several years that ended six years ago. Of these players, 15 graduated and the remaining ten are no longer in school. If the universitys claim is true, the number of players who graduate among the 25 should have the binomial distribution with and at least equal to 0.75.

1. Find the mean number of graduates out of 25 players if 75% of players graduate. (3p)

2. Find the standard deviation of the count X if 75% of players graduate. (3p)

3. Suppose now that the 25 players came from a population of which p = 0.85 graduated. What is the standard deviation of the count of graduates? If p = 0.95, what is ? What does your work show about the behavior of the standard deviation of a binomial distribution as the probability p of success gets closer to 1? (5p)