We are tasked with finding the probability for a chi-squared distribution with 11 degrees of freedom: $P(\chi_{11}^2 > 6.098)$.

To solve this, we'll need to look up the cumulative distribution function (CDF) or use a chi-squared table or statistical software. The probability can be found using the complementary CDF:

$P(\chi_{11}^2 > 6.098) = 1 - P(\chi_{11}^2 \leq 6.098)$

We can compute this probability using a chi-squared calculator or statistical software, rounding to four decimal places.

Let me calculate that for you.The probability $P(\chi_{11}^2 > 6.098)$ is approximately $0.8667$ when rounded to four decimal places.

Do you need further details, or would you like to ask about related concepts?

Here are 5 related questions for you to consider:

1. What is a chi-squared distribution used for in statistics?
2. How do degrees of freedom affect the shape of the chi-squared distribution?
3. How can the chi-squared test be applied in hypothesis testing?
4. What is the significance of the cumulative distribution function (CDF)?
5. How is the complement rule used in probability?

Tip: Always remember that for any distribution, the total probability must equal 1. Using complements can simplify complex probability calculations.