Question 285795: Bear population. To estimate the size of the bear
population on the Keweenaw Peninsula, conservationists
captured, tagged, and released 50 bears. One year later, a
random sample of 100 bears included only 2 tagged bears.
What is the conservationist’s estimate of the size of the
bear population?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! If they tagged 50 bears out of an unknown number of the population, then the number in the population had to be x (unknown).
One year later they take a random sample and they find 2 out of 50 are tagged.
If the ratio of the sample is indicative of the population at large, then a reasonable estimate would be somewhere around:
x/50 = 50/2.
Cross multiply to get:
2x = 2500
x = 1250
The ratio of 50 tagged / 1250 of the total population total is the same as the ratio 2 tagged / 50 of the total sample taken.
This is far from exact, but it is an indication.
More samples, or larger samples, would have to be taken to verify if this is accurate or not.
The length of time between the original tagging and the taking of the samples would have to be short enough so that external factors didn't play into it in a large way (attrition rate of the tagged bears would be one example of an external factor that could impact the results).
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