Question

a countrys department of wildlife hires deion to estimate its wild goat population. deion catches 92 goats, tags them, and releases them. then deion uses binoculars to observe a group of 800 goats, 16 of which are tagged. to the nearest whole number, what is the best estimate for the goat population?

Explanation:

Step1: Set up proportion

Let \( x \) be the total goat population. The proportion of tagged goats in the sample should equal the proportion of tagged goats in the total population. So we have \(\frac{92}{x}=\frac{16}{800}\).

Step2: Solve for \( x \)

Cross - multiply: \( 16x = 92\times800 \). First, calculate \( 92\times800 = 73600 \). Then, \( x=\frac{73600}{16}\).

Step3: Calculate the value

\(\frac{73600}{16}=4600\).

Answer:

4600