In a booming economy, a firm$$s stock is expected to return $17\mathrm{.}7$ percent. It is expected to return $8\mathrm{.}2$ percent in a normal economy and will decline $5$ percent in a recessionary economy. The probability of a recession is $8$ percent while the probability of a boom is $19$ percent. What is the standard deviation of the returns on this stock?

Multiple Choice

$10\mathrm{.}52\%$

$5\mathrm{.}53\%$

$5\mathrm{.}87\%$

$30\mathrm{.}53\%$

$17\mathrm{.}88\%$