Does it make sense to decide between these two investments

Question

Show any work needed.

1. Suppose you are considering two investments, and the critical issues are the rates of return (R₁ and R₂). For Investment 1, the expected rate of return (μ₁) is 10%, and the standard deviation (σ₁) is 3%. For the second investment, the expected rate of return (μ₂) is 20%, and the standard deviation (σ₂) is 12%.

a) Does it make sense to decide between these two investments on the basis of expected value alone? Why or why not?

b) Does it make sense to represent the uncertainty surrounding the rates of return with normal distributions? What conditions do we need for the normal distribution to provide a good fit?

c) Suppose you have decided to use normal distributions (either because of or in spite of your answer to part b). Find the following probabilities:

P(R₁ < 0%)

P(R₂ < 0%)

P(R₁ >20%)

P(R₂ < 10%)