2017-I-11 – Solving Master

Ans: (a) Median

= $ 69

, standard deviation

= $ 7.33

(b)

\frac{2}{5}

Median $= $ 69$ .
Since the range is $$ 22$ , we have

$\begin{array}{rcl} (80 + b) - 61 & = & 22 \\ b & = & 3 \end{array}$

Since the mean is $$ 70$ , we have

$\begin{array}{rcl} \frac{61 + 61 + \dots + 81 + 83 + (70 + a)}{15} & = & 70 \\ a + 1048 & = & 1050 \\ a & = & 2 \end{array}$

Hence, the standard deviation $= $ 7.33$ .
The required probability
$\begin{array}{cl} = & \frac{6}{15} \\ = & \frac{2}{5} \end{array}$