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The problem asks to find the area under the curve of the standard normal distribution between \( z = -1 \) and \( z = 1 \), which corresponds to the area within 1 standard deviation of the mean. Then, it asks to convert this area into a percentage.

### Solution:
For a standard normal distribution (mean 0, standard deviation 1), the area between \( z = -1 \) and \( z = 1 \) is a well-known result in statistics.

1. From the **empirical rule** (or **68-95-99.7 rule**), we know that approximately **68%** of the data lies within 1 standard deviation of the mean in a normal distribution. 

This is the percentage area under the curve between \( z = -1 \) and \( z = 1 \).

Thus, the answer for the blank is:
- **About 68% of the area** lies between \( z = -1 \) and \( z = 1 \).

Would you like more details on the empirical rule or any other related concepts?

### Follow-up Questions:
1. What is the percentage of the area within 2 standard deviations of the mean?
2. How do we calculate the exact area between \( z = -1 \) and \( z = 1 \) using the standard normal table?
3. What is the area under the standard normal curve beyond \( z = 2 \)?
4. How does the standard deviation affect the shape of a normal distribution?
5. Can you explain why the total area under the normal distribution curve is 1?

### Tip:
Always remember that the empirical rule gives you quick approximations for 1, 2, and 3 standard deviations from the mean: 68%, 95%, and 99.7% respectively.

Find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and fill in the blank. About _____% of the area is between z = -1 and z = 1 (or within 1 standard deviation of the mean).

Find out how to calculate the area under the standard normal distribution between z = -1 and z = 1. This problem explores the empirical rule and the percentage of data within 1 standard deviation from the mean, suitable for students in Grades 10-12.

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