A Math test has a mean of 51 and standard deviation of 5.0. Find the corresponding z scores for:
I. a test score of 64
II. a test score of 47
Z = (score-mean)/SD
Insert the values and calculate.
Z = 64-51/5.0 = 13/5.0 = 2.6
Z = 47-51/5.0 = -4/5.0 = -0.8
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To find the corresponding z-scores, we can use the formula:
z = (x - μ) / σ
Where:
- z is the z-score
- x is the test score
- μ is the mean
- σ is the standard deviation
I. For a test score of 64:
z = (64 - 51) / 5.0
z = 13 / 5.0
z = 2.6
So, the z-score for a test score of 64 is 2.6.
II. For a test score of 47:
z = (47 - 51) / 5.0
z = -4 / 5.0
z = -0.8
So, the z-score for a test score of 47 is -0.8.