Find the z-score related to the raw score, mean, and standard deviation as follows. Assume a normal probability distribution.
Z = (score-mean)/SD
To find the z-score related to a raw score, mean, and standard deviation in a normal probability distribution, you can use the following formula:
z = (X - μ) / σ
Where:
- z is the z-score
- X is the raw score
- μ is the mean (or average)
- σ is the standard deviation
To calculate the z-score, you need to subtract the mean from the raw score and then divide the result by the standard deviation.
Let's say, for example, that you want to find the z-score for a raw score of 75, a mean of 80, and a standard deviation of 5. Applying the formula:
z = (75 - 80) / 5
z = -5 / 5
z = -1
So, the z-score for a raw score of 75, given a mean of 80 and a standard deviation of 5, is -1. The negative sign indicates that the raw score is below the mean.