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The question in the image is asking what percentage of the area under the standard normal distribution curve lies between \( z = -2.499 \) and \( z = 2.499 \).

This can be answered by finding the cumulative probability associated with these \( z \)-scores. The standard normal distribution table (or using statistical software) can give us the cumulative probabilities for these \( z \)-values.

1. For \( z = 2.499 \), the cumulative probability is approximately 0.9937.
2. For \( z = -2.499 \), the cumulative probability is approximately 0.0063.

To find the percentage of the area between these two points, subtract the smaller cumulative probability from the larger one:

\[
0.9937 - 0.0063 = 0.9874
\]

Thus, about 98.74% of the area under the curve lies between \( z = -2.499 \) and \( z = 2.499 \).

You should enter 98.74% in the answer box.

Would you like more details on how this calculation works? Let me know if you have any questions.

Here are five related questions you might consider:
1. What does a standard normal distribution represent?
2. How do you use the z-table to find cumulative probabilities?
3. What does the area under the curve between two z-values represent in practical terms?
4. How does changing the z-scores affect the area under the curve?
5. What is the significance of 68-95-99.7 rule in normal distributions?

**Tip:** Always remember that the area under a normal distribution curve represents probabilities, and the total area under the curve equals 1, or 100%.

About ___% of the area under the curve of the standard normal distribution is between z = -2.499 and z = 2.499 (or within 2.499 standard deviations of the mean).

Learn how to calculate the percentage of the area under the standard normal distribution curve that lies between z = -2.499 and z = 2.499. This problem covers key statistical concepts, including the use of z-scores and cumulative probabilities. Suitable for students in Grades 10-12.

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