To estimate the size of a bear population on the Keweenaw Peninsula, conervationist captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist estimate of the size of the bear population?
one out of 50 bears caught is tagged so
50 * 50
To estimate the size of the bear population on the Keweenaw Peninsula, the conservationist used a mark and recapture method. This method involves capturing, tagging, and releasing a certain number of animals and then recapturing a sample to see how many of them are tagged. By analyzing this information, an estimate of the total population size can be determined.
In this scenario, the conservationist initially tagged 50 bears. One year later, a random sample of 100 bears was taken, and it was observed that only 2 of them were tagged.
To calculate the estimated population size, we can use the mark and recapture formula:
Estimated population size = (Total number of individuals in the initial capture) × (Total number of individuals in the second capture) / (Number of tagged individuals recaptured in the second capture)
In this case, the number of bears in the initial capture was 50, the number of bears in the second capture was 100, and the number of tagged bears recaptured was 2.
Plugging these values into the formula:
Estimated population size = (50 × 100) / 2
Estimated population size = 5000 / 2
Estimated population size = 2500
Therefore, based on this mark and recapture method, the conservationist estimates that the size of the bear population on the Keweenaw Peninsula is 2500.