# Solved (Free): The average salary of a male full professor at a public four-year institution offering classes at the doctoral level is

Apr 12, 2021

The average salary of a male full professor at a public four-year institution offering classes at the doctoral level is \$109628. For a female full professor at the same kind of institution, the salary is \$79330. If the standard deviation for the salaries of both genders is approximately \$5200 and the salaries are normally distributed, find the 80th percentile salary for male professors and for female professors. ### Solution Given that the average salary of a male full professor at a public four-year institution offering classes at the doctoral level is$\mu_m= 109628$. A female full professor at the same kind of institution, the average salary is$\mu_f =79330$. The standard deviation for the salaries of both genders is approximately$\sigma = 5200. • Let the 80th percentile for male professor be "a". Then we have  \begin{aligned} & P(X\leq a) =0.8\\ &\Rightarrow P\big(\frac{X-\mu_m}{\sigma} < \frac{a-109628}{5200}\big)=0.8\\ &\Rightarrow P(Z < \frac{a-109628}{5200}\big)=0.8\\ &\Rightarrow \frac{a-109628}{5200}= 0.842\\ &\Rightarrow a = 109628 + 0.842* 5200\\ &\Rightarrow a = 114006.4 \end{aligned}  Thus the 80th percentile salary for male professor is \ $114006.4$.

• Let the 80th percentile salary for Female professors be "b". Then we have

 \begin{aligned} & P(X\leq b) =0.8\\ &\Rightarrow P\big(\frac{X-\mu_f}{\sigma} < \frac{b-79330}{5200}\big)=0.8\\ &\Rightarrow P(Z < \frac{b-79330}{5200}\big)=0.8\\ &\Rightarrow \frac{b-79330}{5200}= 0.842\\ &\Rightarrow b = 79330 + 0.842* 5200\\ &\Rightarrow b = 83708.4 \end{aligned}