To estimate the total number of fur seal pups in Rookery A, you can use the proportion of tagged pups in the observed sample to estimate the total population.
Let:
- \( N \) = total number of fur seal pups in Rookery A.
- \( T \) = number of tagged pups (6704).
- \( O \) = total number of observed pups in the sample (1300).
- \( t \) = number of tagged pups found in the sample (179).
You can set up the proportion as follows:
\[ \frac{t}{O} = \frac{T}{N} \]
Substituting the values gives:
\[ \frac{179}{1300} = \frac{6704}{N} \]
To solve for \( N \), cross-multiply:
\[ 179 \times N = 6704 \times 1300 \]
Now calculate \( 6704 \times 1300 \):
\[ 6704 \times 1300 = 8715200 \]
Now the equation becomes:
\[ 179N = 8715200 \]
Now divide both sides by 179:
\[ N = \frac{8715200}{179} \approx 48645.75 \]
Since the total number of pups must be a whole number, you can round \( N \) to the nearest whole number:
\[ N \approx 48646 \]
Therefore, the estimated total number of fur seal pups in Rookery A is approximately 48,646.