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To calculate the z-score for the person who received a score of 66, we use the formula for the z-score:

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

Where:
- \( X = 66 \) (the person's score)
- \( \mu = 72 \) (the class mean)
- \( \sigma = 2.4 \) (the standard deviation)

Substituting the values:

\[
z = \frac{66 - 72}{2.4} = \frac{-6}{2.4} = -2.5
\]

So, the z-score is \(-2.5000\) (to 4 decimal places).

### Is this unusual?
Generally, a z-score less than \(-2\) or greater than \(+2\) is considered unusual. Since the z-score is \(-2.5000\), this score would be considered unusual.

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Would you like more details or have any further questions?

Here are 5 related questions to expand on this:

1. What does a negative z-score indicate?
2. How is the z-score used to interpret the position of a score in a data set?
3. What does the z-score represent in a normal distribution?
4. Can a z-score be positive, and what does that mean?
5. Why is a z-score of \(\pm2\) considered a boundary for being unusual?

**Tip:** Z-scores are useful for comparing individual scores to the mean, especially when data comes from a normal distribution.

On a recent quiz, the class mean was 72 with a standard deviation of 2.4. Calculate the z-score (to 4 decimal places) for a person who received a score of 66. Is this unusual?

Learn how to calculate a z-score for a person who received a score of 66, given a class mean of 72 and a standard deviation of 2.4. This problem illustrates statistical concepts like z-scores and normal distribution, ideal for high school students (Grades 10-12).

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