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To determine the value of \( k \) such that \( P(X < k) \approx 0.05 \), we need to find the closest cumulative probability from the given cumulative distribution function (CDF) table that is near 0.05.

From the table:

- At \( x = 1 \), \( F(x) = 0.035 \)
- At \( x = 2 \), \( F(x) = 0.051 \)

The probability 0.051 at \( x = 2 \) is closest to 0.05. Therefore, \( k = 2 \).

Would you like more details or have further questions?

Here are five related questions to expand on this topic:
1. What is the definition of a cumulative distribution function (CDF)?
2. How do you interpret the value of a CDF at a specific point?
3. What is the difference between a CDF and a probability mass function (PMF)?
4. How can you estimate probabilities using the CDF graph?
5. How would the value of \( k \) change if the probability were different, say 0.10?

**Tip:** In a CDF, the probability at a particular point represents the cumulative probability up to that point.

Use the given CDF to determine the value k, so that P(X < k) ≈ 0.05.

Learn how to determine the value of k from a CDF table where the probability P(X < k) is approximately 0.05. The table shows cumulative probabilities for different values of x, and the closest match for k is found at x = 2. Suitable for students in grades 9-12.

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