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

a. Construct a table of the estimated probabilities for each GPA€“ probation combination by dividing the number of students in each of the six cells of the table by 500.
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.
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 outcomes selected student has a GPA of 3.5 or above and selected student is on academic probation at the end of the first semester independent outcomes? 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 of 3.5 and above who are on academic probation at the end of the first semester.

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High School GPA 2.5 to 3.0 to 3.5 and 3.5 Above Total Probation 3.0 Yes No Total 50 45 95 30 185 215 135 365 500 135 190