Question

if the mean is 3 and the standard deviation is 1, the z-score associated with a raw score of 4.5

Answer 1

To calculate the z-score for a raw score, you can use the following formula:

\[
z = \frac{(X - \mu)}{\sigma}
\]

where:
- \(X\) is the raw score,
- \(\mu\) is the mean, and
- \(\sigma\) is the standard deviation.

In your case:
- Mean (\(\mu\)) = 3
- Standard deviation (\(\sigma\)) = 1
- Raw score (\(X\)) = 4.5

Now, plug in the values:

\[
z = \frac{(4.5 - 3)}{1} = \frac{1.5}{1} = 1.5
\]

So, the z-score associated with a raw score of 4.5 is **1.5**.