SOLUTION: For a raw score of 20, which combination results in the highest z score? Mean=16 and standard deviation=8 Mean=16 and standard deviation=2 Mean=16 and standard deviation

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Question 1136028: For a raw score of 20, which combination results in the highest z score?
Mean=16 and standard deviation=8
Mean=16 and standard deviation=2
Mean=16 and standard deviation=4
Mean=16 and standard deviation=1

I got mean =16 and standard deviation of 2 as my answers but it was wrong.
thank you in advance!
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the 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.

since the standard deviation is in the denominator, it stand to reason that, if the numerator remains the same, then the fraction with the smallest denominator will be the largest.

that means the standard deviation of 1 will give you the highest z-score.

(x - m) is equal to 20 - 16 which makes the numbeator equal to 4.

4/8 = 1/2
4/2 = 2
4/4 = 1
4/1 = 4 *****