An 8th grade history teached studied the statistics for her mid-term exam. The average grade for the mid-term was 84 points, and the standard deviation was 8 points. The Z-score for a student who scores 90 on the exam is:
84-90/8= -0.75
You have the subtraction backwards
A score of 90 is above the mean, so the z-score should be positive
z-score = (90-84)/8 = +.75
To calculate the Z-score for a student who scored 90 on the exam, you need to use the formula:
Z = (X - μ) / σ
Where:
- X is the value you're interested in (in this case, the score of 90)
- μ is the mean or average score (in this case, 84)
- σ is the standard deviation (in this case, 8)
Plugging in the values, we get:
Z = (90 - 84) / 8
= 6 / 8
= 0.75
So the Z-score for a student who scored 90 on the exam is 0.75.
It seems like the calculation you provided in your question is not correct. The numerator should be (90 - 84), not (84 - 90) as you mentioned. Additionally, the denominator should be 8, not -8 since the standard deviation is a positive value.
Correcting that, the calculation would be:
Z = (90 - 84) / 8
= 6 / 8
= 0.75