Help with normal distribution problem

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May 2nd 2010, 07:25 PM
gtgamer140@yahoo.com

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.
May 2nd 2010, 07:31 PM
pickslides

Quote:

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 $a$ such that

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

Apply the same technique for the second.
May 2nd 2010, 07:46 PM
gtgamer140@yahoo.com

1 Attachment(s)

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.
May 2nd 2010, 08:21 PM
pickslides

Then solve

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

Using symmetry $x_2 =1.2816$

Look here http://davidmlane.com/hyperstat/z_table.html
May 2nd 2010, 09:49 PM
gtgamer140@yahoo.com

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
May 2nd 2010, 09:56 PM
pickslides

Quote:

Originally Posted by gtgamer140@yahoo.com

I don't see where the 0.1 comes from

80% in the middle means 10% each side. (Rofl)
April 3rd 2012, 09:43 AM
callyx

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