To find the \( z \)-score for an ACT score of 20, we need to know the mean (\( \mu \)) and standard deviation (\( \sigma \)) of the ACT scores. Let's assume that the mean ACT score is 21 and the standard deviation is 5, which are typical values.

The formula for the \( z \)-score is:

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

Where:
- \( X \) is the ACT score,
- \( \mu \) is the mean of the ACT scores,
- \( \sigma \) is the standard deviation of the ACT scores.

Plugging in the values:

\[
z = \frac{20 - 21}{5} = \frac{-1}{5} = -0.2
\]

So, the \( z \)-score for an ACT score of 20 is \(-0.2\).

Would you like more details or have any questions?

Here are 5 related questions:
1. What does a negative \( z \)-score indicate in this context?
2. How would the \( z \)-score change if the ACT score was 25 instead of 20?
3. Can you explain what the \( z \)-score represents in terms of standard deviations?
4. How is the \( z \)-score used in determining percentiles?
5. What would be the \( z \)-score if the mean was 23 instead of 21?

**Tip:** The \( z \)-score is useful for comparing scores from different distributions or understanding how far a score is from the mean in terms of standard deviations.

Learn how to calculate the Z-score for an ACT score of 20 using the formula z = (X - mu) / sigma. This problem involves understanding statistics concepts, including mean and standard deviation, and their application in determining a score's position relative to the mean. Suitable for high school students.

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