For Exercises 4.14 and 4.15, see pages 180–181; for 4.16 to 4.20, see pages 183–184; for 4.21 to 4.23, see pages 185–186; for 4.24, see page 187; for 4.25 and 4.26, see page 189; and for 4.27 to 4.29, see page 190.

Question 4.25

4.25 High school rank.

Select a first-year college student at random and ask what his or her academic rank was in high school. Here are the probabilities, based on proportions from a large sample survey of first-year students:

Rank Top 20% Second 20% Third 20% Fourth 20% Lowest 20%
Probability 0.41 0.23 0.29 0.06 0.01
  1. Choose two first-year college students at random. Why is it reasonable to assume that their high school ranks are independent?
  2. What is the probability that both were in the top 20% of their high school classes?
  3. What is the probability that the first was in the top 20% and the second was in the lowest 20%?

4.25

(a) The rank of one student should not affect the other students’ rank as they likely attended different high schools. (b) 0.1681. (c) 0.0041.