In order to keep track of the elephant population in Africa, Kiara catches 82 elephants and marks them. Later, Kiara gets in a helicopter and takes pictures containing 184 elephants. Of the elephants in the pictures, 23 are marked. To the nearest whole number, what is the best estimate for the elephant population?

This problem can be solved using the **capture-recapture method**, a common statistical technique for estimating population sizes in wildlife studies. Here's how the method works:

1. **Mark and Release Step:** Kiara catches and marks 82 elephants.
2. **Recapture Step:** Later, Kiara observes 184 elephants, 23 of which are marked.

We assume that the proportion of marked elephants in the sample (23 out of 184) represents the proportion of marked elephants in the entire population.

Let \( N \) represent the total elephant population in the area. The proportion of marked elephants in the sample should be approximately equal to the proportion of marked elephants in the entire population. This gives us the equation:

\[
\frac{23}{184} = \frac{82}{N}
\]

Now, solve for \( N \):

\[
N = \frac{82 \times 184}{23}
\]

Let's calculate this:

\[
N = \frac{82 \times 184}{23} = \frac{15088}{23} = 656
\]

So, the best estimate for the elephant population is approximately **656 elephants**.

Would you like further details on the steps, or have any other questions?

Here are five related questions for practice:
1. What would happen to the population estimate if only 10 marked elephants were observed?
2. How would the estimate change if Kiara originally marked 100 elephants?
3. If the recaptured group included 30 marked elephants, what would the population estimate be?
4. How can this method be applied to estimate populations of other animals?
5. What assumptions must be true for the capture-recapture method to be accurate?

**Tip:** The capture-recapture method assumes the population is closed, meaning no significant immigration, emigration, births, or deaths occur during the study.

Learn how to estimate the elephant population using the capture-recapture method. Kiara marked 82 elephants, and later, 23 marked elephants were spotted in a sample of 184. Discover how to apply statistical proportions to estimate the total population, ideal for students in Grades 8-10.

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