2012PP-I-15 – Solving Master

Ans: (a)

3

(b) Smaller

Let $σ$ be the standard deviation. By the standard score of Mary, we have
$\begin{array}{rcl} \frac{36 - 48}{σ} & = & - 2 \\ σ & = & 6 \end{array}$

Therefore, the standard score of John

$\begin{array}{cl} = & \frac{66 - 48}{6} \\ = & 3 \end{array}$
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.