a math test has a mean of 43 and a standard deviation of 17.0. find the corrresponding z scores for a test score of 13 and a test score of 59. show work
To find the corresponding z-scores for a test score of 13 and 59, we'll 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
Let's calculate the z-scores for both test scores.
For a test score of 13:
z = (13 - 43) / 17.0
z = -30 / 17.0
z ≈ -1.76
For a test score of 59:
z = (59 - 43) / 17.0
z = 16 / 17.0
z ≈ 0.94
So, the corresponding z-scores for a test score of 13 is approximately -1.76, and for a test score of 59 is approximately 0.94.