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Question $1$

$($Smith$,$ Ch $44\mathrm{.}36)$ The annual returns on U$.$S$.$ corporate stock and U$.$S$.$ Treasury bonds over the next $12$ months are uncertain. Suppose that these returns can be described by normal distributions with U$.$S$.$ corporate stock having a mean of $10\%$ and standard deviation of $12\%,$ and U$.$S$.$ Treasury bonds having a mean of $4\%$ and standard deviation of $5\%.$

a$)$ Which asset is more likely to have a negative return? To answer this question, find $P(x0)$ for each asset class where stock returns $)=10,{}_Q=(12$ and bond returns are $)=4,{}_{}=(5$

b$)$ Draw a diagram of these probabilities.