2016-I-16

Ans: No
Let $\sigma$ be the standard deviation of the scores.

$\begin{array}{rcl}{\displaystyle \frac{22–61}{\sigma }}& =& -2.6\\ -2.6\sigma & =& -39\\ \sigma & =& 15\end{array}$

Let $x$ marks be the score of Mary. Hence, we have

$\begin{array}{rcl}{\displaystyle \frac{x-61}{15}}& =& 1.4\\ x–61& =& 21\\ x& =& 82\end{array}$

The difference of the scores of Mary and Albert

$\begin{array}{cl}=& 82–22\\ =& 60\text{ marks}\\ >& 59\text{ marks}\end{array}$

Therefore, the range of the distribution is at least $60$ marks. The claim is not correct.