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 calculate.
To find the test score that corresponds to a z-score of -1.33, we can use the formula:
z = (X - μ) / σ
where:
- z is the z-score
- X is the value we want to find (the test score)
- μ is the mean of the distribution
- σ is the standard deviation
Given that the mean (μ) is 72 and the standard deviation (σ) is 5, we can plug in these values into the formula:
-1.33 = (X - 72) / 5
To find X, we can rearrange the equation:
-1.33 * 5 = X - 72
-6.65 = X - 72
Adding 72 to both sides of the equation:
-6.65 + 72 = X
65.35 = X
Therefore, the test score that corresponds to a z-score of -1.33 is 65.35.
To find the test score corresponding to a given z-score, 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
In this case, you are given the z-score (-1.33), the mean (72), and the standard deviation (5). Plugging these values into the formula, we can rearrange it to solve for x, the test score:
(-1.33) = (x - 72) / 5
To isolate x, you can multiply both sides of the equation by 5:
(-1.33) * 5 = x - 72
-6.65 = x - 72
Now, add 72 to both sides to get the value of x:
-6.65 + 72 = x
65.35 = x
Therefore, the test score that corresponds to a z-score of (-1.33) is approximately 65.35.