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.