Question

last year over 7000 students took an entrance exam at a certain state university. tammys score was at the 78th percentile. aldos score was at the 56th percentile.
(if necessary, consult a list of formulas.)
(a) which of the following must be true about tammys score?
o tammy scored lower than about 78% of the students who took the exam.
o tammy got about 78% of the questions correct.
o tammy scored higher than about 78% of the students who took the exam.
o tammy got about 78% of the questions wrong.
(b) which of the following must be true about tammys and aldos scores?
o aldo scored higher than tammy.
o both tammy and aldo scored higher than the median
o tammy answered 22 more questions correctly than aldo.
o tammys and aldos scores were both in the bottom half of all scores.

Explanation:

Part (a)

• Percentile Definition: The \(n^{th}\) percentile means that \(n\%\) of the data values are less than or equal to that value. So, if Tammy's score is at the \(78^{th}\) percentile, it means about \(78\%\) of the students scored lower than Tammy.

Part (b)

• Median as \(50^{th}\) Percentile: The median of a data - set is the \(50^{th}\) percentile. Tammy (\(78^{th}\) percentile) and Aldo (\(56^{th}\) percentile) both have percentiles greater than \(50\). So, both scored higher than the median.

Answer:

(a) Tammy scored higher than about \(78\%\) of the students who took the exam.
(b) Both Tammy and Aldo scored higher than the median.