Ans: A
Let $x$ and $y$ be the two test scores, where $x>y$. Let $\bar{x}$ and $\sigma$ be the mean and the standard deviation respectively. Let $z_1$ and $z_2$ be the standard score of the two test scores respectively.
Let $x$ and $y$ be the two test scores, where $x>y$. Let $\bar{x}$ and $\sigma$ be the mean and the standard deviation respectively. Let $z_1$ and $z_2$ be the standard score of the two test scores respectively.
$\left\{\begin{array}{ll}
\dfrac{x-\bar{x}}{\sigma} = z_1 & \ldots \unicode{x2460} \\
\dfrac{y-\bar{x}}{\sigma} = z_2 & \ldots \unicode{x2461}
\end{array}\right.$
$\unicode{x2460} – \unicode{x2461}$, we have
$\begin{array}{rcl}
\dfrac{x-\bar{x}}{\sigma} – \dfrac{y-\bar{x}}{\sigma} & = & z_1 – z_2 \\
\dfrac{x – \bar{x} – y + \bar{x}}{\sigma} & = & z_1 – z_2 \\
\dfrac{x-y}{\sigma} & = & z_1 – z_2 \\
\dfrac{30}{\sigma} & = & 6 \\
\sigma & = & 5
\end{array}$
