Question

salary of full professors the average salary of a male full professor at a public four - year institution offering classes at the doctoral level is $99,685. for a female full professor at the same kind of institution, the salary is $90,330. if the standard deviation for the salaries of both genders is approximately $5200 and the salaries are normally distributed, find the 79th percentile salary for the following. use the standard normal distribution table. round your answers to the nearest dollar and intermediate z - value calculations to 2 decimal places.
part: 0 / 2
part 1 of 2
male professors
the 79th percentile salary for male professors is $

Explanation:

Step1: Find the z - value

We want to find the \(z\) - value corresponding to the 79th percentile. Looking at the standard normal distribution table, the area to the left of \(z\) is \(0.79\). The closest value in the standard normal table gives \(z\approx 0.81\).

Step2: Use the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 99685\) (mean salary for male professors), \(\sigma=5200\) (standard deviation), and \(z = 0.81\).

We need to solve for \(x\). Rearranging the formula gives \(x=\mu+z\sigma\).

Substitute the values: \(x = 99685+0.81\times5200\)

First, calculate \(0.81\times5200=4212\)

Then, \(x=99685 + 4212\)

\(x=103897\)

Answer:

\(103897\)