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The image shows a question regarding standardized tests involving the ACT and SAT. The task is related to finding Z-scores and converting between Z-scores and raw scores. Here's how to solve the parts shown:

### Part (a): Find the Z-score for an ACT score of 19.
The formula for a Z-score is:
\[
Z = \frac{X - \mu}{\sigma}
\]
Where:
- \( X \) is the raw score (19),
- \( \mu \) is the mean (22.2 for the ACT),
- \( \sigma \) is the standard deviation (5.3 for the ACT).

So,
\[
Z = \frac{19 - 22.2}{5.3} = \frac{-3.2}{5.3} \approx -0.60
\]
Thus, the Z-score for an ACT score of 19 is approximately **-0.60**.

### Part (c): Find Jose's ACT score given a Z-score of 0.98.
To find the raw score from a Z-score, use the formula:
\[
X = Z \cdot \sigma + \mu
\]
Where:
- \( Z = 0.98 \),
- \( \mu = 22.2 \) (mean ACT score),
- \( \sigma = 5.3 \) (standard deviation).

So,
\[
X = 0.98 \cdot 5.3 + 22.2 = 5.194 + 22.2 \approx 27.39
\]
Thus, Jose's ACT score is approximately **27.39**.

Would you like more details on any part of the process?

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Here are 5 related questions to expand your understanding:
1. How do Z-scores help in comparing scores from different tests?
2. How would you convert a Z-score to a raw score on the SAT given its mean and standard deviation?
3. What does a negative Z-score indicate about a test score?
4. How do changes in the mean and standard deviation of a test affect Z-scores?
5. Can two people have the same Z-score but different raw scores on different standardized tests?

**Tip**: Z-scores help standardize scores across different distributions, making it easier to compare performances across tests with different scales.

Find the Z-score for an ACT score of 19, and find the ACT score given a Z-score of 0.98.

Learn how to calculate the Z-score for an ACT score of 19, and how to find an ACT score given a Z-score of 0.98. This problem involves using statistical formulas to convert between raw scores and standardized scores, suitable for students in Grades 10-12.

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