Question

last year over 10,000 students took an entrance exam at a certain state university. christines score was at the 76th percentile. juans score was at the 62nd percentile. (if necessary, consult a list of formulas.) (a) which of the following must be true about christines score? christine scored lower than about 76% of the students who took the exam. christine got about 76% of the questions correct. christine scored higher than about 76% of the students who took the exam. christine got about 76% of the questions wrong. (b) which of the following must be true about christines and juans scores? juan scored higher than christine. both christine and juan scored higher than the median. christine answered 14 more questions correctly than juan. christines and juans scores were both in the bottom - half of all scores.

Explanation:

Step1: Recall percentile definition

The $n^{th}$ percentile of a data - set is a value such that $n$ percent of the data values are less than or equal to that value. So, if Christine's score is at the 76th percentile, it means she scored higher than about 76% of the students who took the exam.

Step2: Analyze median and percentiles

The median is the 50th percentile. Since Christine is at the 76th percentile and Juan's percentile is not given completely (but assuming it is also above 50th percentile as no other information suggests otherwise), both Christine and Juan scored higher than the median.

Answer:

(a) Christine scored higher than about 76% of the students who took the exam.
(b) Both Christine and Juan scored higher than the median.