This question has to do with z-scores...
A dean must distribute salary raises to her faculty for next year. She has decided that the mean raise is to be $2000, the standard deviation of raises is to be $400, and the distribution is to be normal. She will attempt to distribute these raises on the basis of merit, meaning that people whose performance is better get better raises. The 5% of the faculty who have done nothing useful in years will receive no more than $ _________ each.

- anonymous

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- amistre64

ahhhh.... standard deviations eh.... where my ti-83 at?

- amistre64

since it is population; we use mu and such right?

- anonymous

yes

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- anonymous

but somehow i need to get a z value or an x value for z=x-mean/sd

- amistre64

2 standards are within the normal right? 95%......

- anonymous

yup

- amistre64

z = x-mu/omega
omega = sqrt(n.p.q) right? and mu=n.p

- anonymous

huh? the standard deviation is already given and so is the mean :S

- amistre64

lol...ok; then mu = 2000 and omega then is 400 right?

- anonymous

yup

- anonymous

and the 5% is the smaller portion of the distribution. but I don't know how to if its the z score that gives you the 0.05 or if its something else

- amistre64

use empiraical rule? gotta similar problem here where sd and mean are given

- amistre64

2000 + 400 is one deviation
2000 + 800 is 2 deviations
2000 + 1200 is 3 deviations right?

- amistre64

those in the out liers are more than 2 standards so they get a raise of 2000 - 1200 = 800 right?

- amistre64

make sense?

- anonymous

yes i think so

- amistre64

<.......-2 sd ........ -1 sd..........mean .........etc

- anonymous

yup

- amistre64

might of gone to far in that but you get the basic premise right?

- anonymous

lol yea

- amistre64

good :) we just went over that in stats class yesterday :)

- anonymous

sweet, so do you have a z table with you?

- amistre64

i got some stuff in my stats book; that might help

- amistre64

table a-2; standard deviation (z) distribution

- anonymous

i have multiple choice answers if it makes a difference. a) 1000, b) 1980, c) 1340 and d)2192 it can't be over 2000 so its one of the
first 3 choices :S

- anonymous

ahh hate stats!

- amistre64

c looks plausible, but cant really say for sure....

- amistre64

2000 - 2(400) = 1200; but thats just an educated guess...

- amistre64

id have to look up how to use a z table to be sure

- amistre64

http://www.intmath.com/counting-probability/z-table.php

- anonymous

well to my understanding, if the 5% is in the smaller portion of the distribution, then you look up0.05 there and get the z score. then just stick that value int he equation and solve for x but its not working

- amistre64

95% falls at the 2 line; and that result is .4772; or 47.72% at most
2000*.4772 = answer maybe? ....954.4 that dint work

- amistre64

http://davidmlane.com/hyperstat/z_table.html
is a calculator for it i think

- amistre64

.02275 is what that gives me

- anonymous

thanks!

- amistre64

what to do with it I aint got a clue lol

- anonymous

hmm it won't let me put the 0.5 anywhere though just keeps saying 0.0000

- anonymous

lol me either.

- amistre64

i put in the mean 2000
the sd 400
and choose below 1200 for the 5%

- amistre64

i got a 1342 on the bottom part of it lol

- anonymous

yea i got that too but i dont really know what it means lol

- amistre64

i think it means pick c :)

- anonymous

lol okay. wth! its only one question haha thank you sooooo much for your help!!

- amistre64

:) hope we are right ;)

- anonymous

me too :D

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