Problem source

The time taken for me to set an acceptable examination question it $T$
hours. The distribution of $T$ is a truncated normal distribution with
probability density $\f$  where
\[
\mathrm{f}(t)=\begin{cases}
\dfrac{1}{k\sigma\sqrt{2\pi}}\exp\left(-\dfrac{1}{2}\left(\dfrac{t-\sigma}{\sigma}\right)^{2}\right) & \mbox{ for }t\geqslant0\\
0 & \mbox{ for }t<0.
\end{cases}
\]
Sketch the graph of $\f(t)$. Show that $k$ is approximately $0.841$
 and obtain the mean of $T$ as a multiple of
$\sigma$.
Over a period of years, I find that the mean setting time is 3 hours.
 \begin{questionparts}                  
\item Find the approximate probability that none of the 16
questions on next year's paper will take more than 4 hours to set.
                       
\item Given that a particular question is unsatisfactory after 2 hours work, 
find the probability that it will still be unacceptable after a further
2 hours work.
\end{questionparts}