On a recent quiz, the class mean was 76 with a standard deviation of 2.7. Calculate the z-score (to 2 decimal places) for a person who received score of 82.
z-score:
Is this unusual?
a.Not Unusual
b.Unusual

To calculate the z-score, we use the formula:

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

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

Given:
- \(x = 82\),
- \(\mu = 76\),
- \(\sigma = 2.7\),

we can plug in the values:

\[
z = \frac{82 - 76}{2.7} = \frac{6}{2.7} \approx 2.22
\]

So, the z-score is approximately **2.22**.

### Is this unusual?
A z-score is generally considered unusual if it falls below -2 or above +2. Since the z-score of 2.22 is greater than 2, it is considered **unusual**.

Answer: **b. Unusual**

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Would you like more details on interpreting z-scores, or do you have any questions?

Here are 5 related questions to explore further:
1. What is the probability of scoring above 82 based on this z-score?
2. How do you interpret a negative z-score?
3. How does changing the standard deviation affect the z-score?
4. What is considered a "usual" range for z-scores?
5. How would the z-score change if the mean increased but the score remained the same?

**Tip:** Z-scores help compare individual scores to the overall distribution, regardless of the scale of the test.

On a recent quiz, the class mean was 76 with a standard deviation of 2.7. Calculate the z-score (to 2 decimal places) for a person who received a score of 82. Is this unusual? a. Not Unusual b. Unusual

Learn how to calculate the z-score for a quiz score of 82, given a class mean of 76 and a standard deviation of 2.7. This step-by-step guide explores z-scores, the empirical rule, and how to determine whether a score is unusual. Suitable for Grades 9-12.

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