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The problem on the screen involves a standard normal distribution. Here is a breakdown of the problem:

1. **Given Information**: 
   - \( Z \) follows a standard normal distribution \( Z \sim N(0, 1) \).
   - The problem asks for the probability that \( Z \) is greater than \( a \), i.e., \( P(Z > a) = 0.2119 \).

2. **Objective**: 
   - Find the value of \( a \).

3. **Solution**:
   - The standard normal distribution table (or using a calculator) is used to find the value \( a \) such that \( P(Z > a) = 0.2119 \).
   - In a standard normal distribution, \( P(Z > a) \) can be found by using \( P(Z < a) = 1 - P(Z > a) \).
   - Therefore, \( P(Z < a) = 1 - 0.2119 = 0.7881 \).
   - Now, you need to find the value of \( a \) such that the cumulative probability up to \( a \) is 0.7881.

4. **Calculation**:
   - Using a standard normal distribution table or a calculator, \( P(Z < 0.8) \) approximately equals 0.7881.

5. **Conclusion**:
   - The value of \( a \) is approximately \( 0.8 \).

Would you like more details or have any other questions? Here are five related questions to consider:

1. How do you calculate probabilities using the standard normal distribution table?
2. What is the significance of the Z-score in a normal distribution?
3. How can you convert a normal distribution to a standard normal distribution?
4. How do you find the area under the curve to the left of a given Z-score?
5. What are common values associated with Z-scores in statistics?

**Tip**: When working with standard normal distributions, it is essential to understand how to read and interpret Z-tables accurately.

A standard normal distribution is given with Z ~ N(0, 1). Find the value of 'a' such that P(Z > a) = 0.2119.

Learn how to find the Z-score 'a' for a given probability in a standard normal distribution, where P(Z > a) = 0.2119. This problem demonstrates the use of standard normal distribution tables and the calculation of cumulative probabilities. Suitable for students in Grades 10-12.

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