Question 1192635
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.


<img src = "http://theo.x10hosting.com/2022/032901.jpg" >