Question

The University of California has two criteria used to set admission standards for freshmen to be admitted to a college in the UC system:

a. Students' GPAs and scores on standardized tests (SATs and ACTs) are entered into a formula that calculates an "admissions index" score. The admissions index score is used to set eligibility standards intended to meet the goal of admitting the top $12\%$of high school students in the state. In this context, what percentile does the top $12\%$represent?

b. Students whoseGPAs are at or above the 96th percentile of all students at their high school are eligible (called eligible in the local context), even if they are not in the top $12\%$of all students in the state. What percentage of students from each high school are "eligible in the local context"?

Short answer

(a) The top $12\%$of students are those who are at or above the ${88}^{th}$percentile of admissions index scores.

(b) The top $4\%$ of students' GPAs are at or above the ${96}^{th}$percentile, making the top $4\%$of students "eligible in the local context".

Step-by-step solution

Given information (part a)

Students' GPAs and scores on standardized tests (SATsand ACTs) are entered into a formula that calculates an "admissions index" score. The admissions index score is used to set eligibility standards intended to meet the goal of admitting the top$12\%$of high school students in the state.

Explanation (part a)

In statistics, the percentiles are the partition values. Percentile divides the entire data into $100$equal parts. The ${50}^{th}$percentiles denote the median and below this value lies $50\%$of data. Similarly, the ${60}^{th}$percentile will have $60\%$of data below it and $40\%$of data above.

In the given context, the admissions index score is used to set eligibility standards intended to meet the goal of admitting the top $12\%$of high school students in the state. Therefore, the top $12\%$of high school students in the state are those who are at or above the ${88}^{th}$percentile of admissions index score.

Given information (part b)

Students whose GPAsare at or above the ${96}^{th}$percentile of all students at their high school are eligible (called eligible in the local context), even if they are not in the top $12\%$of all students in the state.

Explanation (part b)

In statistics, the percentiles are the partition values. Percentile divides the entire data into $100$equal parts. The ${50}^{th}$percentiles denote the median and below this value lies $50\%$of data. Similarly, the ${60}^{th}$percentile will have $60\%$of data below it and $40\%$of data above.

In the given context, students whose GPAs are at or above the ${96}^{th}$percentile of all students in the state. Therefore, the top $4\%$ of the student's GPAs are at or above the ${96}^{th}$percentile, making the top $4\%$of students at their high school "eligible in the local context".