Ans: (a) Median $=\$69$, standard deviation $=\$7.33$ (b) $\dfrac{2}{5}$
- 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
$\begin{array}{rcl}
\dfrac{61 + 61 + \cdots + 81 + 83 + (70 + a)}{15} & = & 70 \\
a + 1048 & = & 1050 \\
a & = & 2
\end{array}$Hence, the standard deviation $=\$7.33$.
- The required probability
$\begin{array}{cl}
= & \dfrac{6}{15} \\
= & \dfrac{2}{5}
\end{array}$
