Question

Twenty-three students took the AP Stats Testand the mean was 82% with a standarddeviation of 3 points. How many studentsearned a score between 79% an 85%?

Answer 1

The mean of the AP stats test is 82% and we have a standard deviation of ±3. If we apply this to the mean of the AP stats test, we have the following values

`\begin{gathered} 82-3=79 \\ 82+3=85 \end{gathered}`

which can be considered as one unit of standard deviation from the mean of the distribution. In this case, we can use the empirical rule of the normal distribution to identify the percentage of students that got scores between 79% to 85%.

According to the rule, if the values are between one unit of standard deviation from the mean, the percentage distribution is 68%. We have 23 students who took the AP stats test, 68% of them belongs to this range, which is

`23*68\%\approx16`

There are 16 students who earned between 79% to 85%.

Answer: 16 students