You are considering the risk$-$return profile of two mutual funds for investment. The relatively risky fund promises an expected return of $11\%$ with a standard deviation of $15\mathrm{.}9\%.$ The relatively less risky fund promises an expected return and standard deviation of $4\mathrm{.}9\%$ and $7\mathrm{.}8\%,$ respectively. Assume that the returns are approximately normally distributed. $[$You may find it useful to reference the z table.$]$

a$-1.$ Calculate the probability of earning a negative return for each fund. $($Round your final answers to $4$ decimal places.$)$

a$-2.$ Which mutual fund will you pick if your objective is to minimize the probability of earning a negative return?

multiple choice $1$

Riskier fund

Less risky fund

b$-1.$ Calculate the probability of earning a return above $8\mathrm{.}9\%$ for each fund. $($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 $8\mathrm{.}9\%?$

multiple choice $2$

Less risky fund

Riskier fund