In the spring, a group of biologists caught and tagged 500 wolves in a wilderness area. These animals were then released. A couple of months later, 200 wolves were caught and 75 of them had tags. Estimate the wolf population in this wilderness area.

Question

Please check if my solution is correct:
75/200 is the percent of wolves caught that had tags;
75/200=500/N
75N=200x500
N=1333.333
Thanks in advance.

Answer 1

Yes, your answer is correct.
To check, compare
75/200=0.375
500/1333.333=0.375

However, biologists use a more elaborate method to calculate.
The proportional method used above assumes replacement of the sample after each recapture, which is not (usually) the case. When the recaptured sample is taken without replacement, the estimate will change, especially when the size of recaptured population is a significant proportion of the whole population. The technique used by biologists uses the hypergeometric distribution.

Fortunately, in this case, the most probable population size is still 1333 using the hypergeometric distribution, so yes, your answer is correct both ways.

Answer 2

Thank you very much.

Answer 3

You're welcome!