Question 1134479
the mean is 14.93%
the standard deviation is 21.74%


you want to know what value of ROE will be exceeded by 78% of the firms.


in a normal distributuion, 78% of the area under the nomral distribution curve to the right of the z-score would generate a z-score equal to -.7721932195.


the z-score formula is z = (x - m) / s


z is the z-score
x is the raw score
m is the raw score mean
s is the standard deviation


this formula becomes -.7721932195 = (x - 14.93) / 21.74.


solve for x to get x = 21.74 * -.7721932195 + 14.93 =  -1.857480591 percent.


this can be seen visually in the following graph.


<img src = "http://theo.x10hosting.com/2019/020906.jpg" alt="$$$" >


78% of the firms will provide a ROE greater than -1.857480591 percent.