Jamal studies orcas and wants to estimate the population in a certain region. Jamal catches 60 orcas, marks them, and releases them. At a later point, Jamal catches 330 orcas and observes that 33 of them are marked. To the nearest whole number, what is the best estimate for the orca population?

To estimate the orca population, we can use the **mark and recapture** method. This method assumes that the proportion of marked orcas in the second sample should be approximately equal to the proportion of marked orcas in the entire population.

Let's define the variables:
- \( N \) = total orca population (what we want to find)
- \( M \) = number of orcas originally marked (60 orcas)
- \( C \) = total number of orcas caught in the second sample (330 orcas)
- \( R \) = number of marked orcas in the second sample (33 orcas)

According to the mark and recapture method, the following proportion holds:

\[
\frac{R}{C} = \frac{M}{N}
\]

Substituting the values:

\[
\frac{33}{330} = \frac{60}{N}
\]

To find \( N \), solve the equation:

\[
N = \frac{60 \times 330}{33}
\]

Now, let's calculate it:

\[
N = \frac{19800}{33} \approx 600
\]

So, the best estimate for the orca population in that region is **600**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How does the mark and recapture method work in different populations?
2. What are the assumptions behind the mark and recapture method?
3. What factors could affect the accuracy of the population estimate?
4. How would the estimate change if Jamal marked a different number of orcas initially?
5. How can statistical methods improve the precision of wildlife population estimates?

**Tip:** When using the mark and recapture method, ensure that the marking does not affect the animal's behavior or chances of being recaptured.

Learn how to estimate the orca population using the mark and recapture method. Jamal catches and marks orcas, then observes marked orcas in a subsequent sample to estimate population size. Calculate the orca population based on given data. Suitable for advanced high school students.

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