Based on the following information, what is the standard deviation of returns?

State of Economy

Recession

Normal

Boom

Probability of state of Economy

$\mathrm{.}22$

$\mathrm{.}47$

$\mathrm{.}31$

Rate of Return if state occurs

$-\mathrm{.}090$

$\mathrm{.}105$

$\mathrm{.}215$

$=>({0\mathrm{.}22}^{**}-\mathrm{.}090)+({\mathrm{.}47}^2\mathrm{.}105)+({\mathrm{.}31}^k\mathrm{.}215)$

$=0\mathrm{.}0962$

A$)10\mathrm{.}97\%$

$\mathrm{.}22C$

B$)12\mathrm{.}04\%$

C$)17\mathrm{.}51\%$

D$)13\mathrm{.}51\%$

E$)16\mathrm{.}05\%$