You are considering the risk$-$return profile of two mutual funds for investment. The relatively risky fund promises an expected return of

$12\mathrm{.}9\%$ with a standard deviation of $16\mathrm{.}7\%.$ The relatively less risky fund promises an expected return and standard deviation of $4\%$ and

$6\mathrm{.}7\%,$ respectively. Assume that the returns are approximately normally distributed.

b$-1.$ Calculate the probability of earning a return above $8\mathrm{.}2\%$ for each fund.

Note: Do not round intermediate calculations. Round your final answers to $4$ decimal places.

b$-2.$ Which mutual fund will you pick if your objective is to maximize the probability of earning a return above $8\mathrm{.}2\%?$

Riskier fund

Less risky fund