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Svetradugi [14.3K]
3 years ago
12

A study of the impact of executive networking on firm performance measured firm performance as annual return on equity​ (ROE), r

ecorded 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.)
Mathematics
1 answer:
vova2212 [387]3 years ago
3 0

Answer:

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 \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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 \mu = 0.1493, \sigma = 0.2174

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 Z = -0.77

So:

Z = \frac{X - \mu}{\sigma}

-0.77 = \frac{X - 0.1493}{0.2174}

X - 0.1493 = -0.77*0.2174

X = -0.0177

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

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