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.