Question

last year over 8000 students took an entrance exam at a certain state university. justins score was at the 24th percentile. melissas score was at the 77th percentile.
(a) which of the following must be true about justins score?
○ justin scored higher than about 76% of the students who took the exam.
○ about 76% of the students who took the exam scored higher than justin.
○ justin got about 24% of the questions correct.
○ justin got about 24% of the questions wrong.
(b) which of the following must be true about justins and melissas scores?
○ melissa scored higher than justin.
○ both justin and melissa scored higher than the median.
○ melissa got 53 more questions correct than justin.
○ justins and melissas scores were both in the bottom half of all scores.

Explanation:

(a)

Step1: Recall the definition of percentile

A \(p\) -th percentile means that \(p\%\) of the data is less than or equal to that value. If Justin is at the \(24^{th}\) percentile, then about \(76\%\) of the students scored higher than him.

(b)

Step1: Analyze the percentile information

Since Justin is at the \(24^{th}\) percentile and Melissa is at the \(77^{th}\) percentile. The median is the \(50^{th}\) percentile. So Melissa scored higher than the median (\(77>50\)) and Justin scored lower than the median (\(24 < 50\)).

Answer:

(a) About \(76\%\) of the students who took the exam scored higher than Justin.
(b) Melissa scored higher than the median.