Question 333728
According to Investment Digest ("Diversification and the Risk/Reward Relationship", Winter 1994, 1-3), the mean of the annual return for common stocks from 1926 to 1992 was 15.4%, and the standard deviation of the annual return was 24.5%. During the same 67-year time span, the mean of the annual return for long-term government bonds was 5.5%, and the standard deviation was 6.0%. The article claims that the distributions of annual returns for both common stocks and long-term government bonds are bell-shaped and approximately symmetric. Assume that these distributions are distributed as normal random variables with the means and standard deviations given previously.
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Find the probability that the return for common stocks will be greater than 9%.
z(0.09) = (0.09-0.154)/0.245 = -0.2612
P(x > 0.09) = P(z> -0.2612) = 0.6930
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Find the probability that the return for common stocks will be greater than 25%.
z(25) = (25-15.4)/24.5 = 0.3918
P(x > 25%) = P(z > 0.3918) = 0.3476
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Cheers,
Stan H.