$1.$ The average return for large$-$cap domestic stock funds over the three years $2011-2014$ was $18\%.$ Assume the $3-$year returns were normally distributed across Large$-$Cap domestic stock funds with a standard deviation of $6\%.$

a$)$ What is the probability an individual large$-$cap domestic stock fund had a three$-$year return of at least $22\%?$

b$)$ How big the return must be for an individual large$-$cap stock fund to outperform $90\%$ of the rest funds?