B

C

D

E

Distribution of Stock Returns

The average return for large$-$cap domestic stock funds over the three years $2009-2011$ was $14\mathrm{.}6\%.$

Assume the three$-$year returns were normally distributed across funds with a standard deviation of $4\mathrm{.}6\%.$

Average return $\%($decimal form$)$

Return standard deviation $\%($decimal form$)$

a$.$ What is the probability an individual large$-$cap domestic stock fund had a three$-$year return of at least $20\%($to $4$ decimals$)?$

b$.$ What is the probability an individual large$-$cap domestic stock fund had a three$-$year return of $10\%$ or less $($to $4$ decimals$)?$

c$.$ How big does the return have to be to put a domestic stock fund in the top $10\%$ for the three$-$year period $($to $2$ decimals$)?$