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To solve the problem, we need to find a **z-score** such that **10% of the total area** is to the **right** of \( z \). This implies that the area to the left of \( z \) is **90%** or **0.9000** of the distribution.

Looking at the **Standard Normal Curve Table** in your image, we’ll find the z-score where the cumulative area (left of z) is closest to **0.9000**.

1. On page 1 of the table, we observe values up to around **0.50** for the cumulative area.
2. On page 2, in the rows for higher z-scores (closer to 1.2, 1.3, and so on), we need to locate a cumulative probability close to **0.9000**.

Upon examining the values:

- **z = 1.28** has a cumulative area of **0.8997**.
- **z = 1.29** has a cumulative area of **0.9015**.

Since **0.8997** (for \( z = 1.28 \)) is closer to **0.9000** than **0.9015** (for \( z = 1.29 \)), we can conclude that:

### Answer:
The approximate z-score satisfying the condition is **1.28**.

Would you like further explanation on how to read the z-table or explore related concepts?

Here are some follow-up questions:
1. How do we interpret z-scores in practical scenarios?
2. How can we use z-scores to compare different data points from various distributions?
3. What is the significance of cumulative areas in the z-table?
4. How does changing the z-score affect the area under the normal curve?
5. Why are z-tables often limited to positive z-scores?

**Tip:** The symmetry of the normal distribution means that negative z-scores can be found by looking at positive z-scores and simply changing the sign.

Find the z-score that best satisfies the condition: 10% of the total area is to the right of z.

Learn how to find the z-score where 10% of the area is to the right, using the standard normal distribution table. This solution demonstrates key statistical concepts, including z-scores and cumulative probability, ideal for undergraduate statistics.

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