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 $6\mathrm{.}5?14\mathrm{.}55\%6\mathrm{.}45\%10\mathrm{.}45\%12\mathrm{.}85\%8\mathrm{.}45\%$