A score that is 6 points below the mean corresponds to a z-score of z= - .50, what is the population standard deviation?
To find the population standard deviation, we need to use the formula for converting a z-score to a raw score.
The formula for converting a z-score to a raw score is:
x = μ + (z * σ)
Where:
- x is the raw score (which is 6 points below the mean in this case)
- μ is the population mean
- z is the z-score
- σ is the population standard deviation (what we are trying to find)
Given that the z-score is -0.50 and the raw score is 6 points below the mean, we can rewrite the formula as:
x = μ - 6
Substituting these values into the formula, we have:
μ - 6 = μ + (-0.50 * σ)
Now we can solve for the population standard deviation, σ.
First, let's simplify the equation:
-6 = -0.50σ
Now divide both sides of the equation by -0.50:
-6 / -0.50 = σ
Simplifying the left side of the equation:
12 = σ
Therefore, the population standard deviation is 12.
To find the population standard deviation, we can use the z-score formula:
z = (x - μ) / σ
In this case, we know that z = -0.50 and x - μ = -6. We want to find σ, which represents the population standard deviation.
Rearranging the formula, we get:
σ = (x - μ) / z
Substituting the given values, we have:
σ = (-6) / (-0.50)
= 12
So, the population standard deviation is 12.
Z = (Score-Mean)/SD
-.5 = (-6)/SD
Solve for SD.