Ans: (a) $3$ (b) Smaller
- Let $\sigma$ be the standard deviation. By the standard score of Mary, we have
$\begin{array}{rcl}
\dfrac{36-48}{\sigma} & = & -2 \\
\sigma & = & 6
\end{array}$Therefore, the standard score of John
$\begin{array}{cl}
= & \dfrac{66-48}{6} \\
= & 3
\end{array}$ - Note that the test score of David is $48$ marks, which is the mean of the distribution. Therefore, the standard deviation will be larger after the deletion. And hence the standard score of John will be smaller.
