Question

to determine the number of deer in a game preserve, a forest ranger catches 880 deer, tags them, and releases them. later 163 deer are caught, and it is found that 88 of them are tagged. assuming that the proportion of tagged deer in the second sample was the same as the proportion of tagged deer in the total population, estimate the number of deer in the game preserve. the number of deer in the game preserve is \\(\square\\).

Explanation:

Step1: Define Variables

Let \( N \) be the total number of deer in the game preserve. The proportion of tagged deer in the total population is \( \frac{880}{N} \), and the proportion of tagged deer in the second sample is \( \frac{88}{163} \).

Step2: Set Up Proportion

Since the proportions are equal, we set up the equation:
\[
\frac{880}{N} = \frac{88}{163}
\]

Step3: Solve for \( N \)

Cross - multiply to get \( 88N = 880\times163 \). Then, divide both sides by 88:
\[
N=\frac{880\times163}{88}
\]
Simplify \( \frac{880}{88}=10 \), so \( N = 10\times163=1630 \).

Answer:

1630