SOLUTION: An investment broker reports that the yearly returns on common stocks are approximately normally distributed with a mean return of 12.4 percent and a standard deviation of 20.6 per

Question 1192635: An investment broker reports that the yearly returns on common stocks are approximately normally distributed with a mean return of 12.4 percent and a standard deviation of 20.6 percent.
What percent of yearly returns are at or below the 10th percentile of the distribution of yearly returns? What percentage are at or above the 10th percentile? Find the 10th percentile of the distribution of yearly returns.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
what i think this means is that you want to know the yearly return that is better than 10% of all the yearly returns, assuming that the yearly returns are normally distributed.
the mean is 12.4% and the standard deviation is 20.6%.
the z-score that has 10% of the area under the normal distribution curve to the left of it is equal to -1.281551567.
the z-score formula is z = (x - m) / s
z; is the z-score
x is the raw score
m is the mean
s is the standard deviation.
the z-score formula becomes:
-1.281551567 = (x - 12.4) / 20.6
solve for x to get:
x = -1.281551567 * 20.6 + 12.4 = -13.99996227.
that's a yearly return of -13.99996227%.
this is what it looks like under the normal distribution curve.

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