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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 2.44 to 1. Of transfer students
who matriculate to the same university, 0.75 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.

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glasstiffany33

Answer:

The proportion of first-time college students who graduated in the top 25% is 2.06:1 , which means there are 2.06 ...

Step-by-step explanation:

Using relations between odds and proportions, it is found that:

a) The proportion who graduated in the top 25 percent of their high  school class is 0.709.

b) For transfer students, the odds in favor of having graduated in the top 25 percent of their high  school class are  3 to 1.

Item a:

  • Odds of 2.44 to 1.
  • To convert an odd a to b to a proportion, the relation is:

[tex]p = \frac{a}{a + b}[/tex]

In this item, [tex]a = 2.44, b = 1[/tex], thus:

[tex]p = \frac{2.44}{2.44 + 1} = \frac{2.44}{3.44} = 0.709[/tex]

The proportion who graduated in the top 25 percent of their high  school class is 0.709.

Item b:

  • Proportion of 0.75, thus:

[tex]0.75 = \frac{a}{a + b}[/tex]

[tex]a = 0.75a + 0.75b[/tex]

[tex]0.25a = 0.75b[/tex]

[tex]a = 3b[/tex]

[tex]b = 1[/tex], thus, [tex]a = 3[/tex]

For transfer students, the odds in favor of having graduated in the top 25 percent of their high  school class are  3 to 1.

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