To solve the probability $P(\chi^2_{85} > 79.355)$, we need to refer to the chi-square distribution table or use a statistical calculator/software since the chi-square distribution is not symmetric.

Given:

• Degrees of freedom ($df$) = 85
• We want to find $P(\chi^2 > 79.355)$

We use the complement rule and look up or calculate the cumulative distribution function (CDF) for the chi-square statistic.

Let me calculate the value.The probability $P(\chi^2_{85} > 79.355)$ is approximately 0.6523.

Would you like further details or explanations on this calculation?

Here are 5 related questions you could explore:

1. What is the meaning of a chi-square distribution?
2. How does the degrees of freedom affect the chi-square distribution?
3. How is the chi-square test used in hypothesis testing?
4. What is the relationship between chi-square values and p-values?
5. How can we interpret a high or low chi-square value?

Tip: Chi-square distributions are particularly useful when testing the fit of observed data to expected outcomes, such as in goodness-of-fit tests.