Of first-time college students who matriculate to a certain university, the odds

Question

Of first-time college students who matriculate to a certain university, the odds in favor of having graduated in the top 25 percent of their high school class are 2.5 to 1. Of transfer students who matriculate to the same university, 0.666666666666667 proportion graduated in the top 25 percent of their high school class.

(a) For first-time college students, the proportion who graduated in the top 25 percent of their high school class is (rounded to three decimal places)

(b) For transfer students, the odds in favor of having graduated in the top 25 percent of their high school class are  to 1.

Explanation / Answer

odds ratio Graduated in top 25 percent of their high school class = 2.5 : 1

Pr(Of transfer students who matriculate to the same university graduated in the top 25 percent of high school class) = 2/3

(a) For first-time college students, the proportion who graduated in the top 25 percent of their high school class is

= 2.5/(2.5 + 1) = 2.5/3.5 = 5/7 = 0.714

(b) Odds  in favor of having graduated in the top 25 percent of their high school class are  to 1 = 2 :(3-2) = 2 : 1  

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