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The question you're working on asks what percentage of the area under the standard normal distribution curve lies outside the interval \([-1.68, 1.68]\) or beyond 1.68 standard deviations from the mean.

To solve this:

1. You can use the Z-table (standard normal distribution table) to find the cumulative probability for \( z = 1.68 \). The table gives the area to the left of \( z = 1.68 \), which is approximately 0.9535 (or 95.35%).

2. Since this is a two-tailed problem (asking for the area outside the interval), the area beyond \( z = 1.68 \) on either side is \( 1 - 0.9535 = 0.0465 \).

3. This 0.0465 is the area in both tails combined, but you want to find the area beyond \( z = 1.68 \) on both the left and right. Since the normal distribution is symmetric, divide the remaining area by 2: 
   \[
   0.0465 \div 2 = 0.02325 \text{ (for each tail)}.
   \]

4. Finally, multiply by 100 to get the percentage: 
   \[
   0.0465 \times 100 = 4.65\%.
   \]

So, about **4.65%** of the area under the curve lies outside the interval \([-1.68, 1.68]\).

Would you like further details or have any questions?

Here are 5 related questions to help you practice or understand further:

1. What percentage of the area lies between \( z = -2 \) and \( z = 2 \)?
2. How do you find the area to the right of a given \( z \)-value using a Z-table?
3. What is the area outside the interval \( z = [-2, 2] \)?
4. Can you explain how the standard normal distribution relates to real-world data distributions?
5. How does the empirical rule (68-95-99.7) relate to standard deviations?

**Tip**: Always double-check whether you're solving for the area inside or outside the interval in these types of problems.

About ___% of the area under the curve of the standard normal distribution is outside the interval z = [-1.68, 1.68] (or beyond 1.68 standard deviations of the mean).

Find out the percentage of the area outside the interval z = [-1.68, 1.68] under the standard normal distribution. This problem covers key statistical concepts such as z-scores and the empirical rule, suitable for Grades 9-12 students.

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