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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.

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.

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.

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".