If George's Z-score is -2 for an exam with a mean score of 72 and a standard deviation of 3. What was his score on the test?

The Z-score formula is given by:

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

Where:
- \( Z \) is the Z-score
- \( X \) is the score
- \( \mu \) is the mean
- \( \sigma \) is the standard deviation

In this case:
- \( Z = -2 \)
- \( \mu = 72 \)
- \( \sigma = 3 \)

We need to solve for \( X \) (George's score):

\[
-2 = \frac{X - 72}{3}
\]

Now multiply both sides by 3:

\[
-6 = X - 72
\]

Add 72 to both sides:

\[
X = 66
\]

So, George's score on the test was **66**.

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. What does a Z-score of -2 indicate in terms of performance?
2. How would George's score change if the standard deviation were 5 instead of 3?
3. What would George's Z-score be if his score was 75 on the same exam?
4. How is the Z-score used in comparing scores across different tests?
5. How do outliers affect the calculation of the mean and standard deviation?

**Tip:** A negative Z-score means the value is below the mean, while a positive Z-score indicates it is above the mean.

If George's Z-score is -2 for an exam with a mean score of 72 and a standard deviation of 3, what was his score on the test?

Learn how to calculate George's score on an exam using the Z-score formula. Given a Z-score of -2, a mean score of 72, and a standard deviation of 3, find out how statistics concepts like standard deviation and Z-scores are applied to solve real-world problems. Suitable for students in Grades 9-12.

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