6.79 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.

Probation High School GPA 2.5 to

,3.0 3.0 to

,3.5 3.5 and Above Total Yes 50 55 30 135 No 45 135 185 365 Total 95 190 215 500

a. Construct a table of the estimated probabilities for each GPA–probation combination. (Hint: See Example 6.25.)

b. Use the table constructed in Part

(a) to approximate the probability that a randomly selected firstyear student at this university will be on academic probation at the end of the first semester.

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?

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?

e. 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.

f. 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.