The problem asks for the probability that a randomly chosen person from those who walked more than 2,500 meters belongs to Group N.

Let's break this down:

1. Total people who walked more than 2,500 meters:

   • People who walked between 2,501 and 5,000 meters: 81
   • People who walked more than 5,000 meters: 68
   • Total: $81 + 68 = 149$

2. People in Group N who walked more than 2,500 meters:

   • People in Group N who walked between 2,501 and 5,000 meters: 35
   • People in Group N who walked more than 5,000 meters: 47
   • Total in Group N who walked more than 2,500 meters: $35 + 47 = 82$

3. Probability calculation: The probability of choosing someone from Group N given they walked more than 2,500 meters is: $\text{Probability} = \frac{\text{People from Group N who walked more than 2,500 meters}}{\text{Total people who walked more than 2,500 meters}} = \frac{82}{149}$

Thus, the correct answer is: $\boxed{C: \frac{82}{149}}$

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How would the probability change if the table had more groups?
2. What is the probability of selecting a person from Group M who walked more than 2,500 meters?
3. How can we calculate the conditional probability for other ranges (e.g., 0 to 2,500 meters)?
4. What are the odds of selecting a person from Group N if everyone is included in the selection?
5. How would the probability change if Group N had 10 fewer people?

Tip: Always ensure that the total number in the denominator corresponds to the specific subset you're focusing on.