Question

an island has 12 fur seal rookeries (breeding places). to estimate the fur seal pup population in rookery a, 4461 fur seal pups were tagged in early august. in late august, a sample of 700 pups was observed, and 277 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 fact that the ratio of tagged pups in the sample to the size of the sample is equal to the ratio of the total number of tagged pups to the total population. So, $\frac{277}{700}=\frac{4461}{x}$.

Step2: Cross - multiply

Cross - multiplying gives us $277x = 4461\times700$.

Step3: Solve for $x$

First, calculate $4461\times700 = 3122700$. Then, $x=\frac{3122700}{277}\approx11273.285$.

Step4: Round to the nearest whole number

Rounding $11273.285$ to the nearest whole number gives $11273$.

Answer:

$11273$