Question

the mean score on a physics test was 75 points. amy’s score was 67 points, which was 2 standard deviations below the mean. what is the variance of the data set? 2 4 8 16

Explanation:

Step1: Find the standard - deviation

We know that Amy's score ($x = 67$) is 2 standard - deviations below the mean ($\mu=75$). Using the formula $x=\mu - k\sigma$, where $k = 2$ (number of standard - deviations), we can solve for $\sigma$.
$67=75 - 2\sigma$.
First, rearrange the equation: $2\sigma=75 - 67$.
$2\sigma = 8$, so $\sigma=\frac{8}{2}=4$.

Step2: Calculate the variance

The variance $\sigma^{2}$ is the square of the standard - deviation.
Since $\sigma = 4$, then $\sigma^{2}=4^{2}=16$.

Answer:

16