The scores on a mathematics test have a mean of 72 and a standard deviation of 5. Find the test score that corresponds to a z-score of (-1.33).
Z = (score-mean)/SD
Insert the values and solve for the score.
To find the test score that corresponds to a given z-score, you can use the formula:
x = μ + (z * σ)
Where:
x = test score
μ = mean
z = z-score
σ = standard deviation
In this case, the mean (μ) is 72, the z-score (z) is -1.33, and the standard deviation (σ) is 5.
Substituting these values into the formula, we can find the corresponding test score:
x = 72 + (-1.33 * 5)
x = 72 - 6.65
x = 65.35
Therefore, the test score that corresponds to a z-score of -1.33 is 65.35.