Worksheet on making inferences from random data with problems involving population estimation.

Final Answer:
400

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Explanation:
We use the capture-recapture method, which is like this:
1. Scientists first catch and tag some animals (here, 20 lions).
2. Later, they catch more animals (160 lions), and see how many of those are tagged (8 lions).

The idea is:
The *proportion* of tagged lions in the second sample should be about the same as the proportion of tagged lions in the whole population.

So:
Tagged in second sample / Total caught in second sample = Tagged originally / Total population

That is:
8 / 160 = 20 / N

Simplify 8/160 = 1/20
So:
1/20 = 20 / N

Now solve for N:
Multiply both sides by N:
N / 20 = 20
Then multiply both sides by 20:
N = 20 × 20 = 400

So the best estimate for the total lion population is 400.