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The image asks for the area under the standard normal distribution curve between \( z = -2 \) and \( z = 2 \), and to convert that area into a percentage.

To solve this:

1. In a standard normal distribution, the total area under the curve is 1, representing 100%. 
2. The area between \( z = -2 \) and \( z = 2 \) corresponds to the probability of a value falling within two standard deviations of the mean.
3. From standard normal distribution tables or a calculator, the cumulative probability for \( z = 2 \) is approximately 0.9772, and for \( z = -2 \), it is 0.0228.
4. The area between \( z = -2 \) and \( z = 2 \) is:
   \[
   0.9772 - 0.0228 = 0.9544
   \]
5. Converting this into a percentage:
   \[
   0.9544 \times 100 = 95.44\%
   \]

So, about **95.44%** of the area is between \( z = -2 \) and \( z = 2 \).

Would you like more details or have any further questions?

Here are 5 related questions for further exploration:
1. What is the area under the normal curve between \( z = -1 \) and \( z = 1 \)?
2. How does the empirical rule (68-95-99.7 rule) apply to normal distributions?
3. How can we calculate areas under the curve for non-standard normal distributions?
4. What is the cumulative probability for \( z = 3 \)?
5. How would the area change if you used a different z-range, like \( z = -3 \) to \( z = 3 \)?

**Tip:** The standard normal distribution tables can be used to find cumulative probabilities for any z-score!

About ___% of the area is between z = -2 and z = 2 (or within 2 standard deviations of the mean).

Learn how to find the area under the standard normal distribution curve between z = -2 and z = 2. This problem uses the empirical rule and cumulative distribution function to determine that approximately 95.44% of the area falls within this range, corresponding to two standard deviations from the mean. Suitable for students in Grades 10-12.

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