An island has 12 fur seal rookeries​ (breeding places). To estimate the fur seal pup population in Rookery​ A, 6704 fur seal pups were tagged in early August. In late​ August, a sample of 1300 pups was​ observed, and 179 of these were found to have been previously tagged. Use a proportion to estimate the total number of fur seal pups in Rookery A.

1 answer

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.