An investor believes that the returns on each of two investments over the next year can be described by a normal distribution with a mean of 10 percent and a standard deviation of 20 percent. This investor also believes that the returns on these two investments are independent. Investment Strategy A is to invest $100,000 in one of these investments, selected at random; Strategy B is to invest $50,000 in each investment. Explain your reasoning when you answer each of the following questions:

a. Which strategy has a larger probability of a return greater than 10 percent?

b. Which strategy has a larger probability of a return greater than 20 percent?

c. Which strategy has a larger probability of a negative return?