You are considering the risk$-$return profile of two mutual funds for investment. The relatively risky fund promises an expected return of $10\mathrm{.}9\%$ with a standard deviation of $15\%.$ The relatively less risky fund promises an expected return and standard deviation of $4\mathrm{.}4\%$ and $7\mathrm{.}3\%,$ respectively. Assume that the returns are approximately normally distributed.

a$-1.$ Calculate the probability of earning a negative return for each fund.

Note: Do not round intermediate calculations. 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 $8\mathrm{.}8\%$ 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 $8\mathrm{.}8\%?$

multiple choice $2$

Riskier fund

Less risky fund