The probability of a boom economy is $20\%,$ the probability of a stable growth economy is $30\%,$ the probability of a stagnant economy is $30\%,$ and the probability of a recession is $20\%.$ The following returns are expected:

Boom: $25\%$ Stable Growth: $10\%$

Stagnant Economy: $5\%.$ Recession: $-15\%$

What is the standard deviation of the following outcomes if the expected $($mean$)$ return is A$\mathrm{.}14\mathrm{.}55\%$ B$\mathrm{.}6\mathrm{.}45\%$ C$\mathrm{.}10\mathrm{.}45\%$ D$\mathrm{.}12\mathrm{.}85\%$ E$\mathrm{.}845\%$