Question

a country in africa is trying to restore its giraffe population and is carefully keeping track of how many giraffes are in the area. to do so, local wildlife authorities put tags on 20 giraffes and release them. later, they corral 570 giraffes; among these giraffes, 15 are tagged. to the nearest whole number, what is the best estimate for the giraffe population?

Explanation:

Step1: Set up proportion

Let $N$ = total population. The ratio of tagged giraffes to total population equals the ratio of tagged giraffes in the sample to sample size:
$$\frac{20}{N} = \frac{15}{570}$$

Step2: Solve for $N$

Cross-multiply to isolate $N$:
$$N = \frac{20 \times 570}{15}$$

Step3: Calculate and round

Compute the value and round to nearest whole number:
$$N = \frac{11400}{15} = 760$$

Answer:

760