Ans: (a) Mean $=36$, mode $=33$ (b) $\dfrac{7}{12}$
- Since the range is $27$, then we have
$\begin{array}{rcl}
49 -(20+a) & = & 27 \\
29 -a & = & 27 \\
a & = & 2
\end{array}$Hence, the mean
$\begin{array}{cl}
= & \dfrac{22+25+25+ \cdots +47+47+49}{24} \\
= & 36 \text{ hours}
\end{array}$and the mode is $33\text{ hours}$.
- The required probability
$\begin{array}{cl}
= & \dfrac{14}{24} \\
= & \dfrac{7}{12}
\end{array}$
