You may attempt this question $3$ more times for credit.

Financial analysts have estimated the returns on shares of the

Woods Corporation and the overall market portfolio under two

economic states nature as follows. For Woods the state dependent

returns are $-0\mathrm{.}01$ in recession, and $0\mathrm{.}04$ in an economic boom. For

the market the state dependent returns are $-0\mathrm{.}04$ in recession, and

$0\mathrm{.}08$ in boom. The analyst estimates that the probability of a

recession is $0\mathrm{.}50$ while the probability of an economic boom is $0\mathrm{.}50.$

Compute the standard deviation of the market.

State your answer in decimal form, working your analysis using at

least four decimal places of accuracy.