Question involving z-scores... I'm really confused

Question

amistre64 · Answer

oy thats alot of words ...

amistre64 · Answer

we have human x-bar, and human S values .. do you know what those refer to?

annipuppi · Answer

I have no idea...

amistre64 · Answer

x-bar is a sample mean

S .... has to be defined in your material somewhere as well.  what would you think it should tell us?

amistre64 · Answer

standard deviation is my guess

amistre64 · Answer

now, there is a formula that should have been presented to you in your course ... it allows us to calcuate a zscore; given a random variable value for x, a sample mean of x-bar, and a standard deviation.

amistre64 · Answer

can you find that zscore formula?

annipuppi · Answer

z score= x-mean/standard deviation

amistre64 · Answer

right

so they give us the values, all we have to do is compute z

for waists,  what are our x, mean, and standard deviation?

amistre64 · Answer

ok, so lets just subtract the means from the dolls; and then divide off the S


     doll: 75.0  56.5  72.0
-mean:-91.2 -80.9 -93.7
------------------------
           -16.2 -24.4 -21.7
     /S     /4.8  /9.8  /6.8
-----------------------
             z1     z2    z3

amistre64 · Answer

i agree with those values

amistre64 · Answer

so what can we consider; given a 95% : 5%  ratio for normaility

amistre64 · Answer

do you recall your empirical rule for approximating with standard deviations?

annipuppi · Answer

Like I said the material isn't comprehensive at all but I know that 95% of the data falls within 2 standard deviations

amistre64 · Answer

that was what i was looking to see :)

so anything less than z=-2 falls outside the range of what is considered 'acceptable' or 'normal'.

do we have any values for z that are less than -2?

annipuppi · Answer

all three values are less than -2

amistre64 · Answer

then we could argue that the dolls proportions exhibit measurements that are less than the acceptable threshold ... they are below the 'minimum' values for normality.  right?

annipuppi · Answer

yes

amistre64 · Answer

of course the wording; "the most different" might suggest that the -3 values are what they are looking to argue with.

how you process this is highly subjective :)

annipuppi · Answer

That's what I figured they meant. Thank you! I actually understand it now!

amistre64 · Answer

good luck :)