Question 1146490: what z-score value identifies each of the following locations in a distribution?
a. Above the mean by 2 standard deviation
b. Below the mean by 1/2 standard deviation
c. Above the mean by 1/4 standard deviation
d. Below the mean by 3 standard deviation
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the z-score itself tells you how many standard deviations you are above or below the mean.
2 above gives you a z-score of 2.
1/2 below gives you a z-score of -.5
1/4 above gives you a z-score of .25
3 below gives you a z-score of -3.
you find this by translating the raw score to the z-score.
for example:
if the mean is 100 and the standard deviation is 20, then 2 standard deviations above the mean should be equal to 140 and the z-score should be 2.
likewise, if the mean is 150 and the standard deviation is 5, then 2 standard deviations above the mean should be equal to 160 and the z-score should stil be 2.
the z-score formula is z = (x-m)/s
z is the z-score
x is the raw score
m is the mean
s is the standard deviation, in this case.
when the mean is 100 and the standard deviation is 20, then z = (140 - 100) / 20 = 40 / 20 equals a z-score of 40/20 = 2.
when the mean is 115 and the standard deviation is 5, then z = (125-115) / 5 = 10 / 5 equals a z-score of 2.
the z-score itself tell you how many standard deviations you are above or below the mean.
if you're above the mean, the z-score will be positive.
if you're below the mean, the z-score will be negative.
a z-score of 0 tells you that you are at the mean.
two different sets of data can have the same z-score, even though the mean the standard deviation can be different.
using the z-score allows you to compare the two different data sets relative position of the raw score from the mean.
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