SOLUTION: ON A HW ASSIGNMENT THE MEAN SCORE WAS 85% WITH A STANDARD DEVIATION OF 4. WHAT ARE THE RAW SCORES FOR EACH OF THE FOLLOWING SCORES? -0.7

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Question 1136027: ON A HW ASSIGNMENT THE MEAN SCORE WAS 85% WITH A STANDARD DEVIATION OF 4. WHAT ARE THE RAW SCORES FOR EACH OF THE FOLLOWING SCORES? -0.7
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
mean is 85 and standard deviation is 4.

formula for z-score is z = (x - m) / s

z is the z-score
x is the raw score
m is the raw mean
s is the standard deviation

formula becomes -.7 = (x - 85) / 4

solve for x to get x = -.7 * 4 + 85

solve for x to get x = -2.8 + 85 = 82.2

the raw score associated with a z-score of -.7 when the mean is 85 and the standard deviation is 4 is equal to 82.2.

here's a visual representation of that.

the first graph shows the area under the normal distribution curve to the left of a raw score of 82.2 when the mean is 85 and the standard deviation is 4.

the second graph shows the area under the normal distribuion curve to the left of a z-score of -.7 when the mean is 0 and the standard deviation is 1.

the same area to the left of it means the raw score and the z-score have the same relative position under the normal distribution curve.

the z-score itself is telling you how many standard deviations you are away from the mean.

a z-score of -.7 means that you are .7 standard deviations to the left of the mean.

if your mean is 85 and your raw score is 82.2 and your standard deviation is 4, then then the difference is -2.8.

to find out how many standard deviations that is from the mean, you divide by the standard deviation to get -2.8 / 4 = -.7

here's the graphs.