Question

the mean score on a physics test was 75 points. amys 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: Calculate the standard deviation

Let the standard deviation be \(\sigma\).
We know that \(x = \mu-2\sigma\), where \(x = 67\) (Amy's score), \(\mu = 75\) (mean).
Substitute the values: \(67=75 - 2\sigma\).
Solve for \(\sigma\):
\(2\sigma=75 - 67\)
\(2\sigma = 8\)
\(\sigma=\frac{8}{2}=4\)

Step2: Calculate the variance

The variance \(\sigma^{2}\).
Since \(\sigma = 4\), then \(\sigma^{2}=4^{2}=16\)

Answer:

16