a math test has a mean of 43 and a standard deviation of 17.0. find the corresponding z scores for a test score of 13 and a test score of 59. show all work.
dfed
To find the corresponding z-scores for a test score of 13 and 59, you 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
First, let's find the z-score for a test score of 13:
z = (13 - 43) / 17.0
z = -30 / 17.0
z ≈ -1.765 (rounded to three decimal places)
Therefore, the z-score for a test score of 13 is approximately -1.765.
Next, let's find the z-score for a test score of 59:
z = (59 - 43) / 17.0
z = 16 / 17.0
z ≈ 0.941 (rounded to three decimal places)
Therefore, the z-score for a test score of 59 is approximately 0.941.