Problem $1.[30$ pts$]$ The operation cost $(D)$ of biological nitrogen removal at a municipal wastewater treatment facility in dollars per year can be obtained by:

$D=3260Q^{0\mathrm{.}87}{C}_{NH4}$

where $Q$ is influent flow rate in million gallons per day $($MGD$)$ and $C_{NH4}$ is influent ammonia

concentration in milligrams per liter $(m\frac{g}{\text{I}}).$ The mean and coefficient of variation of influent flow rate

are $17$ MGD and $0\mathrm{.}24,$ respectively. Assume ammonia concentration is a constant $10m\frac{g}{l}.$

$($a$)$ Compute the second order approximations of the mean and first order approximation of the

variance of annual operation cost for biological nitrogen removal at the facility.

$($b$)$ Assume operation cost $(D)$ is normally distributed. What is the probability that the annual

operation cost exceeds $$500,000$ per year