Find the *z*-score for a SAT score of 581

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To find the z-score for an SAT score of 581, we'll use the same z-score formula:

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

Where:
- \( X \) is the value of the score (in this case, 581).
- \( \mu \) is the mean of the distribution (in this case, 545).
- \( \sigma \) is the standard deviation (in this case, 119).

Substituting the given values:

\[
z = \frac{581 - 545}{119}
\]

\[
z = \frac{36}{119}
\]

\[
z \approx 0.30
\]

So, the z-score for an SAT score of 581 is approximately **0.30**.

Would you like more details or have any questions about this? Here are 5 related questions you might consider:

1. What does a z-score of 0.30 indicate in the context of the SAT score?
2. How would the z-score change if the SAT score was 600 instead of 581?
3. Can you determine the percentile rank for an SAT score with a z-score of 0.30?
4. How can z-scores help in comparing SAT scores across different years?
5. What is the probability of obtaining an SAT score higher than 581 based on its z-score?

**Tip:** When interpreting z-scores, remember that a positive z-score indicates a score above the mean, while a negative z-score indicates a score below the mean.

Learn how to calculate the z-score for an SAT score of 581 using the z-score formula. Understand the concepts of mean and standard deviation in statistics. Suitable for high school students and anyone interested in statistical analysis.

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