Question 5.13

5.13 Do our athletes graduate?

Refer to the setting of Exercise 5.9 (page 250).

  1. Find the mean number of graduates out of 20 players if 80% of players graduate.
  2. Find the standard deviation of the count if 80% of players graduate.
  3. Suppose now that the 20 players came from a population of which graduated. What is the standard deviation of the count of graduates? If , what is ? What does your work show about the behavior of the standard deviation of a binomial distribution as the probability of success gets closer to 1?

5.13

(a) . (b) . (c) . . As gets closer to 1, the standard deviation gets smaller.