While conducting a study on the local weasel population, a scientist caught, tagged, and released 85 weasels. Several weeks later, the scientist caught a total of 800 weasels, of which 20 were tagged. To the nearest whole number, what is the best estimate for the weasel population?

To estimate the weasel population, we can use the **capture-recapture method**, which is based on the assumption that the proportion of tagged weasels in the population remains constant between the two captures.

Let's denote the total weasel population by \( N \).

1. The scientist first tagged and released 85 weasels.
2. Later, the scientist caught 800 weasels, of which 20 were tagged.

The proportion of tagged weasels in the second capture should be approximately equal to the proportion of tagged weasels in the entire population. Mathematically, this can be represented as:

\[
\frac{\text{Number of tagged weasels in the second sample}}{\text{Total weasels in the second sample}} \approx \frac{\text{Number of tagged weasels in the population}}{\text{Total population}}
\]

Substituting the known values:

\[
\frac{20}{800} \approx \frac{85}{N}
\]

Now, solve for \( N \) (the total population):

\[
N \approx \frac{85 \times 800}{20}
\]

\[
N \approx 3400
\]

So, the best estimate for the weasel population, to the nearest whole number, is **3,400**.

Would you like more details on how this estimation method works, or do you have any further questions?

Here are five related questions:
1. How does the capture-recapture method work in more complex ecosystems?
2. What assumptions are made in the capture-recapture method?
3. How would the estimate change if more tagged weasels were found in the second sample?
4. What factors could affect the accuracy of this population estimate?
5. How would you estimate the population if no tagged weasels were recaptured?

**Tip:** When using the capture-recapture method, it's crucial to ensure that the tagging process does not affect the behavior or survival of the animals, as this could skew the results.

Learn how to estimate the weasel population using the capture-recapture method with a detailed step-by-step solution. This problem covers key statistical concepts, including probability and the capture-recapture method formula. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation