The owners of a golf course hired a company to determine how many squirrels were living on their property. First, the company put marks on 172 squirrels. Later, the company returned and counted a total of 346 squirrels, of which 43 were marked. To the nearest whole number, what is the best estimate for the squirrel population?

To estimate the total squirrel population on the golf course, we can use the **capture-recapture method**. This method assumes that the proportion of marked squirrels in the second sample is representative of the proportion of marked squirrels in the entire population.

Let \( N \) be the total squirrel population. The proportion of marked squirrels in the second sample can be expressed as:

\[
\frac{\text{Number of marked squirrels in the second sample}}{\text{Total number of squirrels in the second sample}} = \frac{\text{Number of squirrels initially marked}}{\text{Total population}}
\]

Given:
- Number of marked squirrels initially (\( M \)) = 172
- Number of marked squirrels in the second sample (\( m \)) = 43
- Total number of squirrels in the second sample (\( n \)) = 346

We can set up the proportion as:

\[
\frac{43}{346} = \frac{172}{N}
\]

To find \( N \), solve for \( N \) by cross-multiplying:

\[
43N = 172 \times 346
\]

\[
N = \frac{172 \times 346}{43}
\]

Now calculate \( N \):

\[
N = \frac{172 \times 346}{43} = \frac{59432}{43} \approx 1382
\]

So, the best estimate for the squirrel population on the golf course is approximately **1,382**.

Would you like more details or have any questions?

Here are some related questions to consider:
1. How does the capture-recapture method work in different population studies?
2. What assumptions are necessary for the capture-recapture method to provide accurate estimates?
3. What other methods can be used to estimate wildlife populations?
4. How does the sample size affect the accuracy of population estimates?
5. What are the limitations of the capture-recapture method?

**Tip:** Always ensure that the population is "closed" (no significant changes in the population size between samples) when using the capture-recapture method.

Learn how to estimate the squirrel population using the capture-recapture method with a detailed step-by-step solution. This problem involves applying statistical concepts and formulas to determine population estimates based on marked samples. Suitable for advanced high school students.

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