https://file.aiquickdraw.com/mathbot/file/1727623718835ha02i0cc.jpg

In the image, you're asked to find the z-score for a shaded area of 0.53 under the standard normal distribution. 

To find the z-score for a given area, we use the standard normal distribution table (or Z-table), which provides the cumulative probability corresponding to different z-scores.

### Steps:
1. The area under the curve to the left of the z-score is 0.53. This corresponds to a cumulative probability of 0.53.
2. Using the Z-table, find the closest cumulative probability value to 0.53. The table provides the z-scores for cumulative probabilities.
3. The corresponding z-score for a cumulative probability of 0.53 is approximately **0.08**.

### Conclusion:
The z-score for the shaded region with an area of 0.53 is **0.08**.

Would you like more detailed steps or have further questions on this topic? Here are some related questions you could explore:
1. How to interpret negative z-scores in a normal distribution?
2. How to calculate the area under a curve for a given z-score?
3. How to find the z-score corresponding to a cumulative probability of 0.95?
4. What is the significance of the z-score in hypothesis testing?
5. How do you use the z-score to find probabilities in statistics?

**Tip**: Remember, the Z-table gives you the cumulative probability up to the z-score, so make sure you're interpreting the correct side of the curve (left or right).

Find the z-score for the given shaded region under the standard normal distribution. The shaded area is 0.53.

Learn how to find the z-score for a shaded region with an area of 0.53 under the standard normal distribution. This guide uses Z-tables and the properties of the normal curve to provide a step-by-step solution. Suitable for students studying college-level statistics or advanced high school mathematics.

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