Astudy 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.)

The value of ROE that will be exceeded by 78% of the firms is -1.77%.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

The mean ROE for the firms studied was 14.93% and the standard deviation was 21.74%. This means that

What value of ROE will be exceeded by 78% of the firms?

This is the value of X when Z has a pvalue of 1-0.78 = 0.22.

This is

So:

The value of ROE that will be exceeded by 78% of the firms is -1.77%.