# Thread: Help with normal distribution problem

1. ## Help with normal distribution problem

Don't know how my friend got the z1=-1.28, z2=1.28. Everything else is clear

The question:
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 80th percentile salary for the male professors and female professors. 2. Originally Posted by gtgamer140@yahoo.com Don't know how my friend got the z1=-1.28, z2=1.28. Everything else is clear The question: 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 80th percentile salary for the male professors and female professors.

For the first one,find $\displaystyle a$ such that

$\displaystyle P\left( \frac{a-99,685}{5,200}\right) <0.8$

Apply the same technique for the second.

3. Thank you for your reply but I am looking for an explanation on how my friend obtained the z1 and z2 values. I have attached a picture and circled in red what I meant.

4. Then solve

$\displaystyle P(Z<x_1)= 0.1\implies x_1 = -1.2816$

Using symmetry $\displaystyle x_2 =1.2816$

Look here http://davidmlane.com/hyperstat/z_table.html

5. Thanks again for your post.
I don't see where the 0.1 comes from
Can you explain where exactly my friend gets the 1.2 and .8 from to add and get the separate z values? Everything except that is clear to me
thankx again

6. Originally Posted by gtgamer140@yahoo.com
I don't see where the 0.1 comes from
80% in the middle means 10% each side.

7. ## Re: Help with normal distribution problem

i also do not understand how you got the two z scores. and the answers that were on that persons sheet were wrong to find the 80th percentile you can just go to the TABLE E chart and find the z score that corresponds to .8 which is .7995 which is under .84 so you then times .84(5200)+99685 to get 104,053 and do the same for the female. i am just confused on how you got -1.28 and 1.28