Use a proportion to solve each problem. St. Paul Island in...

Use a proportion to solve each problem. St. Paul Island in Alaska has 12 fur seal rookeries (breeding places). In $1961,$ to estimate the fur seal pup population in the Gorbath rookery, 4963 fur seal pups were tagged in early August. In late August, a sample of 900 pups was observed and 218 of these were found to have been previously tagged. Estimate the total number of fur seal pups in this rookery.

Use a proportion to solve each problem.
St. Paul Island in Alaska has 12 fur seal rookeries (breeding places). In $1961,$ to estimate the fur seal pup population in the Gorbath rookery, 4963 fur seal pups were tagged in early August. In late August, a sample of 900 pups was observed and 218 of these were found to have been previously tagged. Estimate the total number of fur seal pups in this rookery.

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Key Concepts

Cross-Multiplication

Cross-multiplication is an algebraic method used to solve equations involving proportions. By multiplying the numerator of one ratio by the denominator of the other and setting it equal to the product of the remaining numerator and denominator, one can isolate the unknown variable. This technique simplifies the process of solving for an unknown value in proportional relationships.

Proportions

Proportions are mathematical statements that equate two ratios. They are used to set up equivalences between different parts of a problem, allowing for the computation of an unknown variable by ensuring the relationship holds constant. This concept is widely used in scaling situations and estimation problems where a ratio is assumed to remain consistent across different samples or instances.

Capture-Recapture Method

The capture-recapture method is a statistical technique used to estimate the size of a population. It involves capturing a portion of the population, marking or tagging those individuals, and then releasing them back into the population. After allowing time for mixing, a second capture is made, and the proportion of marked individuals in this sample is used to infer the total population size, based on the assumption that the sample is representative.

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