Ans: (a) $12$ (b) No
- The new standard deviation
$\begin{array}{cl}
= & 1.2(10) \\
= & 12 \text{ marks}
\end{array}$ - Let $x$ and $\mu$ be a score and the mean before adjustment. Then after the adjustment, the corresponding score of $x$ and the new mean are $1.2x+5$ and $1.2\mu+5$ respectively.
The standard score of $x$ before adjustment
$\begin{array}{cl}
= & \dfrac{x-\mu}{10}
\end{array}$After adjustment, the standard score of the corresponding mark of $x$
$\begin{array}{cl}
= & \dfrac{(1.2x+5)-(1.2\mu+5)}{12} \\
= & \dfrac{x-\mu}{10} \text{, which is equal to the standard score before adjustment.}
\end{array}$Therefore, there is no change in the standard score.
