Wildlife biologists catch, tag, and release 32 bears at a game reserve. Later, 10 bears are caught and 4 of them have tags. Estimate the total number of bears at the game reserve.

Question

Wildlife biologists catch, tag, and release 32 bears at a game reserve. Later, 10 bears are caught and 4 of them have tags. Estimate the total number of bears at the game reserve.
	A.	320
	B.	316
	C.	128
	D.	80

Bot · Answer

We can use a proportion to estimate the total number of bears at the game reserve:

(number of tagged bears in sample) / (total sample size) = (number of tagged bears in population) / (total population size)

Plugging in the given values, we get:

4/10 = x/32

Solving for x (the estimated total population size):

x = (4/10) * 32
x = 12.8

Rounding to the nearest whole number, we get:

x ≈ 13

Therefore, the best estimate for the total number of bears at the game reserve is 13 x 32 = 416, which is closest to answer choice A, 320.