SOLUTION: A study of the impact of executive networking on firm performance measured firm performance as annual return on equity​ (ROE), recorded as a percentage. The mean ROE for the firm

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Question 1134479: A study of the impact of executive networking on firm performance measured firm performance as annual return on equity​ (ROE), recorded as a percentage. The mean ROE for the firms studied was 14.93​% and the standard deviation was 21.74​%. Assume that these values represent mu and sigma for the population ROE distribution and that this distribution is normal. What value of ROE will be exceeded by 78​% of the​ firms?
The value of ROE that will be exceeded by 78​% of the firms is blank %.
​(Round to two decimal places as​ needed.)
Answer by Theo(13342) About Me  (Show Source):
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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.

$$$

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