Six students took a national standardized test for which the average score was 700 and the standard deviation was 150. If a student’s z-value is 1.75 on the test, what was the student’s score?
To find the student's score, we need to use the formula for z-score:
z = (x - μ) / σ
Where:
z is the z-score,
x is the student's score,
μ is the mean (average) score,
σ is the standard deviation.
Given:
The average score (μ) is 700.
The standard deviation (σ) is 150.
The z-score (z) is 1.75.
Rearranging the formula, we have:
x = z * σ + μ
Substituting the given values:
x = 1.75 * 150 + 700
Calculating:
x = 262.5 + 700
x = 962.5
Therefore, the student's score is 962.5.
To find the student's score, we can use the formula for z-score:
z = (x - μ) / σ
where:
z is the z-score,
x is the student's score,
μ is the population mean, and
σ is the population standard deviation.
In this case, we know the z-value (z = 1.75), the population mean (μ = 700), and the population standard deviation (σ = 150). We want to solve for the student's score (x).
Rearranging the formula, we have:
x = z * σ + μ
Plugging in the values:
x = 1.75 * 150 + 700
Calculating the result:
x = 262.5 + 700
x = 962.5
Therefore, the student's score is 962.5.
Z = (score-mean)/SD
Insert values and calculate.