Question $3$:

$($a$)$ Determine the hydrologic risks of a $50-$year flood occurring during the $30,50,$ and $100$ years of service lives of a project. For full points show calculations clearly with numbers at least four decimal places. $(15$ points$)$

$($b$)$ The mean, standard deviation, skew of the log transformed discharges of the upstream San Joaquin River are $3\mathrm{.}50,0\mathrm{.}50,$ and $0\mathrm{.}30$ respectively, where the discharges are in $f\frac{t^3}{s}.$ Compute the $50-$year and $100-$year peak discharges. Find the table for frequency factors at the end of this exam.

For full points show calculations clearly with numbers at least four decimal places. $(10$ points$)$