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 zequalsminus1 and zequals1 ​(or within 1 standard deviation of the​ mean).


To find the percentage of the area under the standard normal distribution curve between \( z = -1 \) and \( z = 1 \) (within 1 standard deviation of the mean), we follow these steps:

1. **Look up the z-values in a standard normal distribution table**:
   - The cumulative area to the left of \( z = 1 \) is approximately **0.8413**.
   - The cumulative area to the left of \( z = -1 \) is approximately **0.1587**.

2. **Find the area between \( z = -1 \) and \( z = 1 \)**:
   - The area between these two z-values is the difference:
   \[
   0.8413 - 0.1587 = 0.6826
   \]

3. **Convert to percentage**:
   - Multiply by 100 to convert the area to a percentage:
   \[
   0.6826 \times 100 = 68.26\%
   \]

Thus, **about 68.26%** of the area is between \( z = -1 \) and \( z = 1 \), or within 1 standard deviation of the mean.

Would you like more details or have any questions?

### Related Questions:
1. What is the area under the curve between \( z = -2 \) and \( z = 2 \)?
2. How do you calculate the area under the normal curve for any given z-score?
3. What is the probability of getting a z-score greater than 2?
4. How can you interpret z-scores in a normal distribution?
5. What percentage of data falls within 2 standard deviations of the mean in a normal distribution?

**Tip:** The area under the standard normal curve for any z-score represents the cumulative probability or proportion of values below that z-score.

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).

This guide explains how to find the area between z = -1 and z = 1 in a standard normal distribution curve and convert it to a percentage. Using key concepts like Z-scores and the empirical rule, this solution is ideal for students in Grades 10-12 learning about probability and statistics.

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