Assume the annual returns of Fund a are normally distributed with a mean and standard deviation of…

Assume the annual returns of Fund a are normally distributed with a mean and standard deviation of 30%. The annual returns of Fund B are also normally distributed, but with a mean and standard deviation of 40%. The returns of both funds are independent of each other. What is the mean and standard deviation of the difference of the returns of the two funds, Fund B minus Fund A? At the end of the year, Fund B has returned 80%, and Fund A has lost 12%. How likely is it that Fund B outperforms Fund A by this much or more?

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