Question

In a sampling expedition near a peninsula, 180 dolphins from a large population of dolphins were captured and marked by tagging their dorsal fins. The tagged dolphins were then allowed to join back into the population. In a subsequent expedition, 42 dolphins were photographed from the same large population. Among these, 7 dolphins contained the tags. Assuming that the population size remains the same and that tags were not lost, the estimated population size of dolphins in the peninsula is ........... (answer in integer)

Hint:

The Mark and Recapture method estimates population size by assuming that the proportion of tagged individuals in a sample is the same as the proportion in the entire population.

Answer 1

Step 1: Understanding the method.
This problem involves the use of the Mark and Recapture method to estimate the population size of animals. The formula for this method is: \[ \frac{M}{N} = \frac{m}{n} \] Where:
- \( M \) = number of dolphins initially tagged = 180
- \( N \) = total estimated population size (what we are solving for)
- \( m \) = number of tagged dolphins in the second sample = 7
- \( n \) = total number of dolphins in the second sample = 42
Step 2: Substituting the known values into the equation.
We can rearrange the formula to solve for \( N \): \[ N = \frac{M \times n}{m} \] Substituting the values: \[ N = \frac{180 \times 42}{7} = \frac{7560}{7} = 1080 \] Final Answer: \[ \boxed{1080} \]