An island has 12 fur seal rookeries (breeding places). To estimate the fur seal pup population in Rookery A, 5742 fur seal pups were tagged in early August. In late August, a sample of 900 pups was observed, and 217 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

An island has 12 fur seal rookeries​ (breeding places).  To estimate the fur seal pup population in Rookery​ A, 5742 fur seal pups were tagged in early August.  In late​ August, a sample of 900 pups was​ observed, and 217 of these were found to have been previously tagged.  Use a proportion to estimate the total number of fur seal pups in Rookery A.

GPT 3.5 · Answer

Let x be the total number of fur seal pups in Rookery A.

We can set up the proportion:

5742 (total tagged pups) / x = 217 (previously tagged in sample) / 900 (total in sample)

Cross multiplying, we get:

5742 * 900 = 217x

x = (5742 * 900) / 217
x = 23916

Therefore, the estimated total number of fur seal pups in Rookery A is 23,916.