Question

an island has 12 fur seal rookeries (breeding places). to estimate the fur seal pup population in rookery a, 4812 fur seal pups were tagged in early august. in late august, a sample of 600 pups was observed, and 295 of these were found to have been previously tagged. use a proportion to estimate the total number of fur seal pups in rookery a.
the estimated total number of fur seal pups in rookery a is
(round to the nearest whole number.)

Explanation:

Step1: Set up the proportion

Let $x$ be the total number of fur - seal pups in Rookery A. The proportion is based on the ratio of tagged seals in the sample to the size of the sample being equal to the ratio of the total number of tagged seals to the total population. So, $\frac{295}{600}=\frac{4812}{x}$.

Step2: Cross - multiply

Cross - multiplying gives us $295x = 4812\times600$.

Step3: Calculate the right - hand side

$4812\times600 = 2887200$. So, $295x=2887200$.

Step4: Solve for $x$

$x=\frac{2887200}{295}\approx9787.12$.

Step5: Round to the nearest whole number

Rounding $9787.12$ to the nearest whole number gives $9787$.

Answer:

$9787$