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.

Question

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.

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

yes

anonymous · Answer

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

amistre64 · Answer

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

anonymous · Answer

yup

amistre64 · Answer

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

anonymous · Answer

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

amistre64 · Answer

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

anonymous · Answer

yup

anonymous · Answer

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 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

make sense?

anonymous · Answer

yes i think so

amistre64 · Answer

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

anonymous · Answer

yup

amistre64 · Answer

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

anonymous · Answer

lol yea

amistre64 · Answer

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

anonymous · Answer

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

amistre64 · Answer

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

amistre64 · Answer

table a-2; standard deviation (z) distribution

anonymous · Answer

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 · Answer

ahh hate stats!

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

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 · Answer

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 · Answer

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

amistre64 · Answer

.02275 is what that gives me

anonymous · Answer

thanks!

amistre64 · Answer

what to do with it I aint got a clue lol

anonymous · Answer

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

anonymous · Answer

lol me either.

amistre64 · Answer

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

amistre64 · Answer

i got a 1342 on the bottom part of it lol

anonymous · Answer

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

amistre64 · Answer

i think it means pick c :)

anonymous · Answer

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

amistre64 · Answer

:) hope we are right ;)

anonymous · Answer

me too :D