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To solve this problem, we need to determine the z-score that corresponds to a shaded area of 0.65 under the standard normal distribution curve. The shaded region likely represents the cumulative probability to the left or right of a particular z-value.

### Steps to find the z-score:
1. **Cumulative Area**: Since the shaded area is 0.65, this means that the cumulative probability (area under the curve from the far left up to the z-score) is 0.65.
2. **Use a z-table or statistical tool**: You can use a z-score table (or inverse normal distribution function) to find the z-score that corresponds to this cumulative probability.
   - If you look up 0.65 in the cumulative z-table, it corresponds to a z-score of approximately **0.39**.

Thus, the z-score that corresponds to a cumulative area of 0.65 is **0.39** (rounded to two decimal places).

### Would you like further clarification or details on how to use a z-score table? 

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Here are 5 follow-up questions:
1. What is the formula for converting raw scores to z-scores?
2. How would the z-score change if the shaded area was 0.85?
3. Can you explain the relationship between z-scores and probability distributions?
4. What is the significance of a z-score in hypothesis testing?
5. How does the central limit theorem relate to the use of z-scores?

#### Tip:
When using z-tables, ensure you know whether the given area represents the cumulative probability from the left or the tail to find the right corresponding z-score.

Find the z-score for the given shaded region under the standard normal distribution. Shaded Area = 0.65.

Learn how to find the z-score for a shaded area of 0.65 under the standard normal distribution curve. This example covers key statistical concepts such as z-scores, cumulative probability, and normal distribution tables.

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