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.