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The image you've uploaded displays a normal distribution curve, with two vertical lines at z-scores \( z = -0.23 \) and \( z = 1.96 \), indicating the bounds of the shaded region under the curve. The problem is asking for the area of the shaded region, which corresponds to the probability between these two z-scores.

To find the area, follow these steps:

1. **Find the cumulative probability for each z-score** using the standard normal distribution table or a calculator:
   - For \( z = -0.23 \), the cumulative probability \( P(Z \leq -0.23) \) is approximately 0.4090.
   - For \( z = 1.96 \), the cumulative probability \( P(Z \leq 1.96) \) is approximately 0.9750.

2. **Subtract the cumulative probabilities** to find the area between the two z-scores:
   \[
   P(-0.23 \leq Z \leq 1.96) = P(Z \leq 1.96) - P(Z \leq -0.23)
   \]
   \[
   = 0.9750 - 0.4090 = 0.5660
   \]

Thus, the area of the shaded region is approximately **0.5660**, which represents the probability that a value falls between \( z = -0.23 \) and \( z = 1.96 \) on the standard normal distribution.

Would you like more details or have any questions on this? Here are five follow-up questions:

1. How is the z-score calculated from raw data?
2. What is the significance of the cumulative distribution function (CDF) in probability?
3. How would the area change if the z-scores were further apart?
4. How do we interpret the area under the curve in real-world scenarios?
5. What is the total area under the standard normal curve?

**Tip:** The total area under a normal distribution curve is always 1 (or 100%), representing the total probability of all possible outcomes.

Find the area of the shaded region between z-scores -0.23 and 1.96 on the standard normal distribution.

Learn how to calculate the area between z-scores -0.23 and 1.96 on the standard normal distribution. Using cumulative probabilities, the area represents the probability that a value falls between these z-scores, approximately 0.5660. This step-by-step guide applies key statistical concepts suitable for high school students.

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