A person has a raw score of 89 on a test where the population mean is 80 and the
population standard deviation is 2.80. Calculate the Z score for this individual’s raw
score.

To calculate the Z-score for a raw score, the formula is:

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

Where:
- \(X\) is the raw score (89),
- \(\mu\) is the population mean (80),
- \(\sigma\) is the population standard deviation (2.80).

Substituting the values:

\[
Z = \frac{89 - 80}{2.80} = \frac{9}{2.80} \approx 3.21
\]

The Z-score is approximately **3.21**.

This means the individual's score is 3.21 standard deviations above the mean.

Would you like more details or have any questions?

Here are 5 related questions:
1. What does a positive Z-score signify in a dataset?
2. How would the Z-score change if the standard deviation increased?
3. Can you calculate the percentile rank from this Z-score?
4. What if the population mean changed to 85 but the raw score stayed the same?
5. How is the Z-score used in hypothesis testing?

**Tip:** A higher Z-score indicates that the score is farther away from the mean in a positive direction.

A person has a raw score of 89 on a test where the population mean is 80 and the population standard deviation is 2.80. Calculate the Z score for this individual’s raw score.

Learn how to calculate the Z-score for a raw score of 89, with a population mean of 80 and a standard deviation of 2.80. This problem demonstrates statistical concepts such as Z-scores, standard deviation, and how to interpret results. Suitable for students in Grades 9-12.

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