Question

an island has 12 fur seal rookeries (breeding places). to estimate the fur seal pup population in rookery a, 5079 fur seal pups were tagged in early august. in late august, a sample of 700 pups was observed, and 160 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 \(\frac{\text{Number of tagged in sample}}{\text{Size of sample}}=\frac{\text{Total number of tagged}}{\text{Total population}}\).
We know that the number of tagged in the sample is \(160\), the size of the sample is \(700\), and the total number of tagged is \(5079\). So the proportion is \(\frac{160}{700}=\frac{5079}{x}\).

Step2: Cross - multiply

Cross - multiplying gives us \(160x = 700\times5079\).
First, calculate \(700\times5079=700\times(5000 + 79)=700\times5000+700\times79=3500000+55300 = 3555300\).
So, \(160x=3555300\).

Step3: Solve for \(x\)

Then \(x=\frac{3555300}{160}=22220.625\).

Answer:

\(22221\)