91Ó°ÊÓ

Referring to the Journal of Accounting Public Policy (Vol. 34, 2015) study impact of executive networking on firm performance, exercise 2.101,

The firm performance is measured as annual return on equity (ROE), recorded as a percentage, i.e., x follows a normal distribution with a mean of 13.93 and a standard deviation of 21.65.

x follows a normal distribution with a mean of 13.93 and a standard deviation of 21.65, i.e.$\mathrm{μ}=13.93   and   \mathrm{σ}=21.65$

The value of return on equality (ROE), i.e., a is,

$\begin{array}{rcl}P\left(x<a\right)& =& 0.8\\ P\left(\frac{x-\mathrm{μ}}{\mathrm{σ}}<\frac{a-\mathrm{μ}}{\mathrm{σ}}\right)& =& 0.8\\ P\left(z<\frac{a-13.93}{21.65}\right)& =& 0.8\\ \mathrm{Φ}\left(\frac{a-13.93}{21.65}\right)& =& 0.8\\ & & \end{array}$

$\begin{array}{rcl}\frac{a-13.93}{21.65}& =& {\mathrm{Φ}}^{-1}\left(0.8\right)\\ a& =& 13.93+\left(21.65×{\mathrm{Φ}}^{-1}\left(0.8\right)\right)\\ a& =& 13.93+\left(21.65×0.7881\right)  \left[From S\tan dard Normal Table\right]\\ a& =& 13.93+17.0624\\ a& =& 30.9924\\ & & \end{array}$

$a=30.9924$

So, the value of a is 30.9924.

Therefore, the return on equality (ROE) value that will be exceeded by 80% of the firms is 30.9924.