Consider three stock funds, which we will call Stock Funds $1,2,$ and $3.$ Suppose that Stock Fund $1$ has a mean yearly return of $17\mathrm{.}80$

percent with a standard deviation of $12\mathrm{.}40$ percent; Stock Fund $2$ has a mean yearly return of $13\mathrm{.}90$ percent with a standard deviation

of $14\mathrm{.}00$ percent, and Stock Fund $3$ has a mean yearly return of $7\mathrm{.}20$ percent with a standard deviation of $16\mathrm{.}50$ percent.

$($a$)$ For each fund, find an interval in which you would expect $95\mathrm{.}44$ percent of all yearly returns to fall. Assume returns are normally

distributed. $($Round your answers to $2$ decimal places. Negative amounts should be indicated by a minus sign.$)$

$($b$)$ Using the intervals you computed in part a$,$ compare the three funds with respect to average yearly retConsider three stock funds, which we will call Stock Funds $1,2,$ and $3.$ Suppose that Stock Fund $1$ has a mean yearly return of $17\mathrm{.}80$

percent with a standard deviation of $12\mathrm{.}40$ percent; Stock Fund $2$ has a mean yearly return of $13\mathrm{.}90$ percent with a standard deviation

of $14\mathrm{.}00$ percent, and Stock Fund $3$ has a mean yearly return of $7\mathrm{.}20$ percent with a standard deviation of $16\mathrm{.}50$ percent.

$($a$)$ For each fund, find an interval in which you would expect $95\mathrm{.}44$ percent of all yearly returns to fall. Assume returns are normally

distributed. $($Round your answers to $2$ decimal places. Negative amounts should be indicated by a minus sign.$)$

$($b$)$ Using the intervals you computed in part a$,$ compare the three funds with respect to average yearly returns and with respect to

variability of returns.urns and with respect to

variability of returns.