You are an investment advisor and a client asks you to tell her the chance of...

You are an investment advisor and a client asks you to tell her the chance of making money on an investment at the end of the year. You gather data on annual rates of return for the investment and find that they have a normal distribution with a mean of 5% and a standard deviation of 6%. Determine the probability that the client loses money on the investment at the end of the year, to three decimal places. Hint: If the client "loses money", what must the return be smaller than?

0.983 0.797 0.352 -0.833 0.203

Expert Solution

X : Annual rate of return for the investment

X follows normal distribution with a mean of 5% and a standard deviation of 6%

Client loses money if Annual rate of return for the investment is negative i.e < 0 i.e X< 0

Probability that the client loses money on the investment at the end of the year = P(X<0)

Z-score for 0 = (0-mean)/standard deviation = (0-5)/6 =-5/6 = -0.83

From standard normal normal tables,

P(Z<=-0.83) = 0.203

P(X<0) = P(Z<-0.83)=0.203

Probability that the client loses money on the investment at the end of the year = P(X<0) = 0.203

Probability that the client loses money on the investment at the end of the year = 0.203

Answer:

0.203

Standard normal table:

orchestra answered 2 years ago

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