the mean score on a physics test was 75 points. amys score was 67 points, which was 2 standard deviations…
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? o 2 o 4 o 8 o 16
Answer
Explanation:
Step1: Find the standard - deviation
Let the standard - deviation be $\sigma$. We know that Amy's score $x = 67$ is 2 standard deviations below the mean $\mu=75$. So, $\mu - 2\sigma=x$. Substituting the values, we get $75−2\sigma = 67$. Solve for $\sigma$: [ \begin{align*} 75−2\sigma&=67\
- 2\sigma&=67 - 75\ -2\sigma&=-8\ \sigma& = 4 \end{align*} ]
Step2: Calculate the variance
The variance $\text{Var}(X)=\sigma^{2}$. Since $\sigma = 4$, then $\text{Var}(X)=4^{2}=16$.
Answer:
16