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This image shows a question related to the normal distribution, with a shaded region under the bell curve. The x-axis is labeled, and the given z-value is -2.52, corresponding to the left tail of the normal distribution. The problem is asking for the area of the shaded region, which corresponds to the cumulative probability for z ≤ -2.52.

To solve this:
1. We need to use a **z-table** or a **standard normal distribution calculator** to find the cumulative probability corresponding to a z-value of -2.52.
   
2. From the **z-table**, the cumulative area (or probability) to the left of z = -2.52 is approximately **0.00594**. This value represents the area of the shaded region under the curve to the left of -2.52.

Thus, the area of the shaded region is approximately **0.0059**.

Let me know if you'd like more details on how the z-table works or how to find this area using a calculator!

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Here are 5 questions that build upon this:
1. What is the total area under the standard normal distribution curve?
2. How do you interpret the cumulative probability for a given z-value?
3. How would you calculate the area for z-values greater than 0?
4. How does the symmetry of the normal distribution help in calculating probabilities for negative z-values?
5. What is the area between two z-values, for example, between z = -2 and z = 2?

**Tip:** When using a z-table, remember that it only gives you the cumulative probability for negative z-values. For positive z-values, use symmetry or subtract from 1.

Learn how to calculate the area of the shaded region under the standard normal distribution curve for z = -2.52. This problem involves key statistical concepts such as the Z-score and the standard normal distribution. Suitable for students in Grades 10-12.

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