https://file.aiquickdraw.com/mathbot/file/1729832291728xwcv8fis.jpg

The image you've uploaded shows standard normal distribution (Z-score) tables, which give the areas under the normal curve corresponding to different Z-scores. 

You mentioned calculating the area between the mean and a Z-score of -1.11. Let's work through this:

1. **Find the Z-score in the table**: The Z-score is -1.11. The tables typically only list positive Z-scores, but because the standard normal curve is symmetric, we can look up the value for +1.11 and use that result for the negative Z-score as well.
   
2. **Locate the value for Z = 1.11**:
   - From the table, for Z = 1.11, the area under the curve from 0 to Z = 1.11 is approximately **0.3665**.

3. **Conclusion**: The area under the curve between the mean (Z = 0) and Z = -1.11 (or Z = 1.11 by symmetry) is **36.65%** or **0.3665**.

Would you like more details or clarifications on this process?

Here are five relative questions:
1. How would you calculate the area between two Z-scores, such as Z = -1.11 and Z = 1.11?
2. How is the symmetry of the normal distribution helpful in solving problems like this one?
3. What would the area be if the Z-score were -1.5 instead of -1.11?
4. How can this table be used to find areas above a given Z-score?
5. How is the total area under the normal curve related to probability?

**Tip**: Remember that the total area under a standard normal curve is always 1 (or 100%), representing the full probability.

What is the percentage of the area under a normal curve between the mean and -1.11 standard deviations?

Learn how to calculate the area under a normal curve for Z = -1.11 using standard normal distribution tables. This guide walks you through the steps, including how symmetry is used to find the area for negative Z-scores. Suitable for high school students (Grades 9-12).

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