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?
Based on studies of populations, we can expect the number of bears in the sample to represent the general population in proportion. Write a proportion to express this relationship letting the number of bears in the total population be b.
Use the ratio of tagged bears to total number of bears in the proportion.
Write the proportion:
2 = 50
Solve the proportion for b:
2b = 5000
b = 2500
We can expect that there are 2,500 bears in the Keweenaw Peninsula.