An island has 12 fur seal rookeries​ (breeding places).  To estimate the fur seal pup population in Rookery​ A, 6022 fur seal pups were tagged in early August.  In late​ August, a sample of 1200 pups was​ observed, and 173 of these were found to have been previously tagged.  Use a proportion to estimate the total number of fur seal pups in Rookery A.
Question content area bottom
Part 1
The estimated total number of fur seal pups in Rookery A is 
  
enter your response here.

We can solve this problem using a proportion based on the method of capture-recapture, often used in estimating animal populations. The idea is to assume that the proportion of tagged pups in the sample is representative of the proportion of tagged pups in the entire population.

Let:

- \( N \) be the total number of fur seal pups in Rookery A (the unknown we want to estimate).
- 6022 is the number of tagged pups.
- 1200 is the size of the observed sample.
- 173 is the number of tagged pups found in the sample.

We set up the proportion:

\[
\frac{\text{Tagged pups in the sample}}{\text{Sample size}} = \frac{\text{Total tagged pups}}{\text{Total population}} 
\]

\[
\frac{173}{1200} = \frac{6022}{N}
\]

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

\[
173N = 6022 \times 1200
\]

\[
173N = 7,226,400
\]

\[
N = \frac{7,226,400}{173} 
\]

\[
N \approx 41,766
\]

So, the estimated total number of fur seal pups in Rookery A is approximately **41,766**.

Would you like more details or have any questions?

Here are five related questions to explore:

1. How does the capture-recapture method work in other contexts?
2. What are the assumptions behind using proportions for population estimates?
3. What are potential sources of error in this type of population estimate?
4. How can we adjust for errors in sampling when estimating populations?
5. How would the estimate change if the number of tagged pups found in the sample increased or decreased?

**Tip:** Always check if the sample is random and representative when using proportions for population estimates.

An island has 12 fur seal rookeries​ (breeding places). To estimate the fur seal pup population in Rookery​ A, 6022 fur seal pups were tagged in early August. In late​ August, a sample of 1200 pups was​ observed, and 173 of these were found to have been previously tagged. Use a proportion to estimate the total number of fur seal pups in Rookery A.

Learn how to estimate the total population of fur seal pups in Rookery A using the capture-recapture method. Given 6022 tagged pups and a sample of 1200 observed pups, this problem covers essential concepts of population estimation and proportions. Ideal 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