Question

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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: Find deviation from mean

$75 - 67 = 8$

Step2: Calculate standard deviation

Let $\sigma$ = standard deviation. Since $8 = 2\sigma$, solve for $\sigma$:
$\sigma = \frac{8}{2} = 4$

Step3: Compute variance

Variance is $\sigma^2$:
$\sigma^2 = 4^2 = 16$

Answer:

16