A park ranger's team tags 6 wolverines. A month later, they catch 5 wolverines of which 2 have tags. Estimate the number of wolverines that live in the park.

2/5 = 6/x

Cross multiply and solve for x.

Thank you.

You're welcome.

To estimate the number of wolverines in the park, we can use a concept called "mark and recapture." This method is commonly used in wildlife population estimation.

The idea behind mark and recapture is that if a subset of a population is captured, tagged, released back into the population, and then recaptured at a later time, we can estimate the total population size based on the proportion of tagged individuals in the recaptured sample.

Here's how we can apply this method to estimate the number of wolverines in the park:

1. In the first tagging event, the park ranger's team tags 6 wolverines. This serves as the "marked" population.

2. A month later, the team recaptures a sample of wolverines. Out of the 5 recaptured wolverines, only 2 have tags. Let's call this number "x."

3. The proportion of tagged wolverines in the recaptured sample is calculated by dividing the number of tagged individuals by the total sample size. In this case, x out of 5 is tagged, so the proportion is 2/5 or 0.4.

4. Assuming that the recaptured sample is representative of the entire wolverine population, we can estimate the total population size using the Lincoln-Petersen index. The formula is:

Population size estimate = (Total number marked in initial sample) * (Total number caught in second sample) /Number caught with tags in second sample

Substituting the given values, we get:

Population size estimate = (6) * (5) / (2) = 15

Therefore, based on this estimation method, the number of wolverines living in the park is approximately 15. It's important to note that this is just an estimate and there might be some assumptions and limitations associated with it.