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Please help me to answer a Finance Question

發問:

Suppose that the returns on an investment are normally distributed with an expected return of 10% and standard deviation of 5%. What is the likelihood of making a positive return? (Hint: the area under a curve for 1 std dev is 34.13%, 2 std dev is 47.73%, and 3 std dev is 49.87%.)

最佳解答:

The mean is 10%. 2 x standard deviation = 2 x 5% = 10%. So anything smaller than negative two standard deviations will give you negative return (return < 0%). If we just focus on the side of positive returns, the prob. is 47.73% +50% = 97.73%. Or, there is a chance of 2.27% that a loss is resulted.

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