z-score in a given distribution is -.50.  If the mean of this distribution is 130 and the standard deviation is 20, the equivalent raw score in that distribution is

To find the equivalent raw score given the z-score, mean, and standard deviation, we use the formula:

\[
X = \mu + (z \times \sigma)
\]

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

Given:
- Mean (\(\mu\)) = 130,
- Standard deviation (\(\sigma\)) = 20,
- Z-score (\(z\)) = -0.50,

We substitute the values into the formula:

\[
X = 130 + (-0.50 \times 20)
\]
\[
X = 130 - 10
\]
\[
X = 120
\]

So, the equivalent raw score is **120**.

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. How would you calculate the raw score if the z-score was +1.25?
2. If the mean were changed to 140 but the z-score remained -0.50, what would the raw score be?
3. What is the z-score formula for converting raw scores back to standardized scores?
4. If the standard deviation was 15 instead of 20, how would that affect the raw score calculation?
5. What does a z-score of 0 mean in terms of the raw score?

**Tip:** A negative z-score indicates that the raw score is below the mean, while a positive z-score indicates it is above the mean.

z-score in a given distribution is -.50. If the mean of this distribution is 130 and the standard deviation is 20, the equivalent raw score in that distribution is

Find out how to calculate the raw score when the z-score is -.50, the mean is 130, and the standard deviation is 20. This statistical problem introduces key concepts such as z-scores, raw scores, and standard deviation. Suitable for students in Grades 10-12.

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