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This question is asking for the value of \( c \) in a standard normal distribution where:

\[
P(Z > c) = 0.1949
\]

### Steps to solve:

1. **Identify the probability**: Here, we are given that the probability \( P(Z > c) = 0.1949 \). This means the area to the right of \( c \) under the standard normal curve is 0.1949.

2. **Find the complement**: Since the total area under the curve is 1, the area to the left of \( c \) is:
   \[
   P(Z \leq c) = 1 - 0.1949 = 0.8051
   \]
   So, \( P(Z \leq c) = 0.8051 \).

3. **Use the Z-table or calculator**: You can now look up the Z-value that corresponds to an area of 0.8051 in the cumulative distribution table for the standard normal distribution.

   From the Z-table, we find that:
   \[
   c \approx 0.86
   \]

Therefore, the value of \( c \) is approximately **0.86** when rounded to two decimal places.

Would you like further clarification on any part of the solution? Here are some related questions for more practice:

1. What is the interpretation of the standard normal distribution?
2. How do you find \( P(Z < c) \) from a Z-table?
3. Can you explain the relationship between probabilities and areas under the normal curve?
4. How do Z-scores help in finding probabilities?
5. What is the inverse cumulative distribution function?

**Tip**: Always check whether you're dealing with the upper tail (as in this case) or the lower tail when working with probabilities.

Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c so that P(Z > c) = 0.1949.

Learn how to calculate the value of Z such that P(Z > c) = 0.1949 in a standard normal distribution. This problem covers key probability concepts, including cumulative distribution functions and properties of the standard normal distribution. Suitable for students in Grades 10-12.

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