Question

an island has 12 fur seal rookeries (breeding places). to estimate the fur seal pup population in rookery a, 6042 fur seal pups were tagged in early august. in late august, a sample of 1200 pups was observed, and 153 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: Define variables and proportion

Let \( x \) be the total number of fur seal pups in Rookery A. The proportion of tagged pups in the sample should equal the proportion of tagged pups in the total population. So we have the proportion: \(\frac{\text{tagged in sample}}{\text{sample size}}=\frac{\text{total tagged}}{\text{total population}}\), which is \(\frac{153}{1200}=\frac{6042}{x}\).

Step2: Solve for \( x \)

Cross - multiply to get \( 153x = 1200\times6042 \). First, calculate \( 1200\times6042 = 7250400 \). Then, solve for \( x \) by dividing both sides of the equation by 153: \( x=\frac{7250400}{153} \).

Step3: Calculate the value of \( x \)

\( \frac{7250400}{153}=47388.235\cdots \). Rounding to the nearest whole number, we get \( x\approx47388 \).

Answer:

47388