The Lottery Commission Has Designed a New Instant Lottery Game $$\begin{array} { | c | c | } \hline X & P [ X ] \\\hline 0 & 0.95 \\\hline 10 & 0.049 \\\hline 100 & 0.001 \\\hline\end{array}$$

The lottery commission has designed a new instant lottery game. Players pay $1.00 to scratch a ticket, where the prize won, X, (measured in $) has the following discrete probability distribution : $$\begin{array} { | c | c | } \hline X & P [ X ] \\\hline 0 & 0.95 \\\hline 10 & 0.049 \\\hline 100 & 0.001 \\\hline\end{array}$$ Which of the following best describes the standard deviation of X ? $$\begin{array} { | l | l | } \hline \text { A. } & 14.552 \text { in } \$ ^ { 2 } \\\hline \text { B. } & 3.815 \text { in } \$ \\\hline \text { C. } & 0.348 \text { in } \$ \\\hline \text { D. } & \text { None of these choices are correct } \\\hline\end{array}$$