To find \( P(Z > 0.16) \), we use the standard normal distribution table or a calculator that provides the cumulative distribution function (CDF) for the standard normal distribution.

1. First, find \( P(Z \leq 0.16) \) using the CDF:
   - From the Z-table or calculator, the value of \( P(Z \leq 0.16) \) is approximately **0.5636**.

2. To find \( P(Z > 0.16) \), we use the fact that:
   \[
   P(Z > 0.16) = 1 - P(Z \leq 0.16)
   \]

   Therefore:
   \[
   P(Z > 0.16) = 1 - 0.5636 = 0.4364
   \]

Thus, \( P(Z > 0.16) \) is **0.4364** (rounded to 4 decimal places).

Would you like further clarification or details on this? 

Here are some related questions:
1. What is the probability \( P(Z > 1.5) \)?
2. How do you find \( P(Z \leq -0.16) \)?
3. What is the relationship between the standard normal distribution and other normal distributions?
4. How do you calculate \( P(a < Z < b) \) for given values of \( a \) and \( b \)?
5. Can you explain the symmetry property of the standard normal distribution?

**Tip:** The standard normal distribution is symmetric about zero, meaning \( P(Z > x) = P(Z < -x) \).

Learn how to find the probability P(Z > 0.16) using the standard normal distribution table or a calculator. This solution involves key concepts in probability, such as the cumulative distribution function (CDF) and the complement rule. The result is P(Z > 0.16) = 0.4364. Suitable for students in Grades 10-12.

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