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A young investment manager tells his client that the probability of making a positive return with...

A young investment manager tells his client that the probability of making a positive return with his suggested portfolio is 75%. If it is known that returns are normally distributed with a mean of 4.8%, what is the risk, measured by standard deviation, that this investment manager assumes in his calculation? (You may find it useful to reference the z table. Round "z" value and final answer to 3 decimal places.)

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Answer #1

For normal distribution, P(X < A) = P(Z < (A - )/)

Here, = 4.8%

P(X > 0) = 0.75

P(X < 0) = 1 - 0.75 = 0.25

P(Z < (0 - 4.8)/) = -0.674

-4.8)/ = -0.674

= 7.122%

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