Question

Multiple choice: Select the best answer. Mark receives a score report detailing his performance on a statewide test. On the math section, Mark earned a raw score of $39$, which placed him at the 68th percentile. This means that

(a) Mark did better than about $39\%$ of the students who took the test.

(b) Mark did worse than about $39\%$ of the students who took the test.

(c) Mark did better than about $68\%$of the students who took the test.

(d) Mark did worse than about $68\%$ of the students who took the test.

(e) Mark got fewer than half of the questions correct on this test.

Short answer

The correct option is (c).

Step-by-step solution

Step 1. Given

Mark has received his test score report, which details his performance. Marks received a raw score of $39$, putting him in the $68th$ percentile.

Step 2. Concept

The pth percentile of a distribution is the value with p percent of the observations less than it.

Step 3. Explanation 

Percentiles are used to determine the percentage of values that fall below a specific data value. In this case, Mark's position reveals that $68\%$of the students scored lower than Mark. As a result, the correct option is (c).