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The image contains a problem that appears to be about determining the value of a variable given a probability and a normal distribution table.

### Problem Statement:
You are likely asked to determine the value of a variable \( Z \) (often referred to as the Z-score) associated with a certain probability in the context of the standard normal distribution.

### General Approach:
1. **Identify the Probability:** The probability is given, and you need to find the corresponding Z-value from the standard normal distribution table.

2. **Use the Z-table:** The Z-table gives the area (or probability) to the left of a given Z-score in a standard normal distribution. Depending on the exact problem, you may need to find the Z-score corresponding to a cumulative probability.

3. **Determine the Z-Score:**
   - If the probability is given as \( P(Z \leq z) = p \), find \( z \) in the Z-table where the cumulative probability equals \( p \).
   - If the probability is for the right tail \( P(Z > z) = p \), you would find the Z-score corresponding to \( 1 - p \) in the table.

### Example Calculation:
Let's say the problem gives you a probability of \( P(Z \leq z) = 0.975 \) and asks for the Z-value.

- **Step 1:** Look up the probability \( 0.975 \) in the Z-table.
- **Step 2:** The closest value in the Z-table to \( 0.975 \) is typically around \( z = 1.96 \).

Thus, the Z-score corresponding to \( P(Z \leq z) = 0.975 \) is approximately \( z = 1.96 \).

If you can specify the exact probability or further clarify the problem, I can provide a more tailored solution.

Do you have any questions or need more details on how to use the Z-table? Here are five related questions for further exploration:

1. How would you find the Z-score corresponding to a different cumulative probability, such as \( P(Z \leq z) = 0.90 \)?
2. What is the Z-score if the cumulative probability is \( P(Z \geq z) = 0.025 \)?
3. How would you calculate the probability for a non-standard normal distribution?
4. Can you explain the relationship between Z-scores and standard deviations in the normal distribution?
5. How does the shape of the normal distribution change as the mean or standard deviation changes?

**Tip:** When working with Z-tables, remember that they typically provide the cumulative probability from the far left of the distribution up to a specific Z-score.

Learn how to determine the Z-score from a given probability in the context of the normal distribution. This problem involves using the Z-table to find the corresponding Z-score for a given cumulative probability. Suitable for advanced high school students and anyone interested in statistics.

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