# Thread: Need help with this question, very tricky

1. ## Need help with this question, very tricky

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 73rd percentile salary for the male professors and female professors.

I'm a new user here, and i found a similar thread here:
Help with normal distribution problem

Stuck figuring out this question

2. ## Re: Need help with this question, very tricky

You need to know the z-score associated with the 73rd percentile. Do you have a chart or table? Are you using a percentile to z-score calculator? Depending on the method you use, you will find that the appropriate z-score is 0.6128 (or something close, depending on the number of significant figures your table or chart uses). So, how do you find a z-score.

$z = \dfrac{x - \mu}{\sigma}$

So, plug in the values you know:

$0.6128 = \dfrac{x - 99685}{5200}$ to find the 73rd percentile salary for male professors and
$0.6128 = \dfrac{x - 90330}{5200}$ to find the 73rd percentile salary for female professors.

In each case, solve for $x$

3. ## Re: Need help with this question, very tricky

So, for the 73th percentile, it's 0.6128, and yeah im using the z chart

5. ## Re: Need help with this question, very tricky

That's the chart i'm using.

6. ## Re: Need help with this question, very tricky

Then I gave you your answer. Just solve for x in the two equations I posted.