Question $8$

An investment in company I has an expected return of $$150,000$ and a standard deviation of $$30,000.$ An investment in company II has an expected return of $$175,000$ and a standard deviation of $$40,000.$ If the returns are normally distributed and independent, what is the probability that the return from company II is at least $$50,000$ more than the return from company I?

A $0\mathrm{.}206$

B $0\mathrm{.}309$

C $0\mathrm{.}453$

D $0\mathrm{.}611$