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To solve the problem, we need to find the z-value corresponding to the area of 0.9920 to the right of the z-score, which implies that the area to the left of this z-score is:

\[
1 - 0.9920 = 0.0080
\]

Next, using a Standard Normal Distribution Table (Z-table), we find the z-score that corresponds to a cumulative probability of 0.0080. This is typically found by looking for the value in the table that matches or is closest to 0.0080.

From the Z-table, the z-score corresponding to a cumulative probability of 0.0080 is approximately:

\[
z \approx -2.41
\]

Thus, the z-value that corresponds to the given area is approximately **-2.41**.

Would you like more details on how to read the Z-table or any other explanation?

Here are 5 related questions you might find useful:
1. What does a z-score represent in a standard normal distribution?
2. How do you use the Z-table to find areas under the curve?
3. What is the significance of cumulative probability in normal distribution problems?
4. How does symmetry of the standard normal curve help in finding z-scores?
5. Can you calculate z-scores using technology, and if so, how?

**Tip:** In a standard normal distribution, the total area under the curve is always 1, and this is key to interpreting probabilities.

Find the z value that corresponds to the given area in the figure below. Use the Standard Normal Distribution Table and enter the answer to 2 decimal places. The area to the right is 0.9920.

Learn how to find the z-score corresponding to a given area in a standard normal distribution. This problem involves using the Z-table to determine the z-value when the area to the right is 0.9920. Suitable for students in Grades 10-12.

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