A country in Africa is trying to restore its zebra population and is carefully keeping track of how many zebras are in the area. To do so, local wildlife authorities put tags on 140 zebras and release them. Later, they corral 450 zebras; among those zebras, 30 are tagged. To the nearest whole number, what is the best estimate for the zebra population?

To estimate the zebra population using the capture-recapture method, we apply the same logic as in the previous example.

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

1. The wildlife authorities tagged and released 140 zebras.
2. Later, they corralled 450 zebras, of which 30 were tagged.

The proportion of tagged zebras in the second sample should be approximately equal to the proportion of tagged zebras in the entire population:

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

Substituting the known values:

\[
\frac{30}{450} \approx \frac{140}{N}
\]

Now, solve for \( N \):

\[
N \approx \frac{140 \times 450}{30}
\]

\[
N \approx 2100
\]

So, the best estimate for the zebra population, to the nearest whole number, is **2,100**.

Would you like further details on this method or have any other questions?

Here are five related questions:
1. How might the time between tagging and recapturing affect the estimate?
2. What would be the impact on the population estimate if fewer tagged zebras were recaptured?
3. How can the accuracy of the capture-recapture method be improved?
4. What are the potential biases in the capture-recapture method?
5. How does this method apply to estimating populations of endangered species?

**Tip:** Ensure the time between the initial tagging and subsequent recapture is appropriate—long enough for the zebras to mix but not so long that tags are lost or animals migrate out of the area.

Learn how to estimate the zebra population using the capture-recapture method with a step-by-step solution. Wildlife authorities tagged and released 140 zebras and later corralled 450 zebras, of which 30 were tagged. Discover how to apply statistics and probability to estimate wildlife populations accurately. 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