$1.$ Consider a call center that receives its demand over a set of different travel websites. The weekly demand for each website is normally distributed with a mean and standard deviation given in Table $1.$ Develop an $\backslash ($ R $\backslash )$ script that creates a simulation with $100,000$ trials to determine total call center demand.

Table $1$: Weekly demand for travel sites $($in hours$)$

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|\}$

$\backslash$hline $\backslash$begin$\{$tabular$\}\{$c$\}$

Travel $\backslash \backslash$

Site

$\backslash$end$\{$tabular$\}$ & Mean & $\backslash$begin$\{$tabular$\}\{$c$\}$

Standard $\backslash \backslash$

Deviation

$\backslash$end$\{$tabular$\}\backslash \backslash$

$\backslash$hline A & $200$ & $20\backslash \backslash$

$\backslash$hline B & $50$ & $10\backslash \backslash$

$\backslash$hline C & $100$ & $15\backslash \backslash$

$\backslash$hline D & $150$ & $30\backslash \backslash$

$\backslash$hline E & $100$ & $30\backslash \backslash$

$\backslash$hline F & $100$ & $10\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

a$)$ What are the mean and standard deviation of total call center demand according to your simulation?

b$)$ Develop a histogram that models the risk profile for total call center demand.