In a class of 50 students, Sarah scored in the 85th percentile on her final exam. What does this mean about Sarah's performance?(C:1)

Question

BlackTom AI · Accepted Answer

First, let's restate what the question is asking: interpreting what it means for Sarah to be in the 85th percentile on a final exam in a class of 50 students.
Option a: 'Sarah scored higher than or equal to 85% of the students.' This is the standard interpretation of the 85th percentile: Sarah performed as well as or better than roughly 85% of her peers. In a group of 50, 85% corresponds to 0.85 × 50 = 42.5 students, so Sarah is at or above the performance of about 42 or 43 students, which aligns with the percentile concept.
Option b: 'Sarah scored higher than 85 of the students.' Saying higher than 85 students would imply she is above 85/50, which is impossible since there are only 50 students. This indicates a misunderstanding of percentile terminology and is incorrect.
Option c: 'Sarah’s score is in the top 15 students of the class.' The top 15 students correspond to the top 30% of the distribution in a 50-student class (15/50 = 30%). Being in the 85th percentile places her in the top ~15% of performers, not necessarily within the top 15 students overall given the discrete class size; furthermore, the percentile definition is about relative standing across the distribution, not a fixed count of students. This makes this option imprecise and misleading.
Option d: 'Sarah’s score is equal to or below 85% of the students.' This would place Sarah at or below the 85th percentile, which contradicts being at the 85th percentile. Since the percentile indicates a higher relative standing, this statement is incorrect.
Overall, option a is the only statement that correctly reflects the meaning of the 85th percentile in this context, while options b, c, and d misinterpret percentile concepts or apply them inaccurately.

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