Provide an Appropriate Response $\begin{array}{|c|c|}\hline x & P(x) \\\hline 0 & 0.37 \\1 & 0.13 \\2 & 0.06 \\3 & 0.15 \\4 & 0.29 \\\hline\end{array}$

Provide an appropriate response. Round to the nearest hundredth.
-Find the standard deviation for the given probability distribution. $\begin{array}{|c|c|}\hline x & P(x) \\\hline 0 & 0.37 \\1 & 0.13 \\2 & 0.06 \\3 & 0.15 \\4 & 0.29 \\\hline\end{array}$

A) $\sigma = 2.90$
B) $\sigma = 1.70$
C) $\sigma = 2.52$
D) $\sigma = 1.81$