Chapter 6.7, Problem 90E

Use the information given in the previous exercise to answer the following questions.

1. a. Estimate the proportion of first-year students with high school GPAs between 2.5 and 3.0 who are on academic probation at the end of the first semester.
2. b. Estimate the proportion of those first-year students with high school GPAs 3.5 and above who are on academic probation at the end of the first semester.

6.89 Five hundred first-year students at a state university were classified according to both high school GPA and whether they were on academic probation at the end of their first semester. The data are summarized in the accompanying table.

1. a. Construct a table of the estimated probabilities for each GPA–probation combination. (Hint: See Example 6.25.)
2. b. Use the table constructed in Part (a) to approximate the probability that a randomly selected first-year student at this university will be on academic probation at the end of the first semester.
3. c. What is the estimated probability that a randomly selected first-year student at this university had a high school GPA of 3.5 or above?
4. d. Are the two events selected student has a high school GPA of 3.5 or above and selected student is on academic probation at the end of the first semester independent events? How can you tell?