70 tagged, released; 450 caught, 25 tagged; est. population

willmon13

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so im gonna write the question i have. if im doing this wrong please help me!!!

Problem: A regional forestry division wanted to estimate the number of deer in a particular national park. They caught and tagged 70 deer and released them back into the park. Later they selected a sample of 450 deer. Of the 450 deer, 25 were tagged. Assuming that the proportion of tagged deer in the sample holds for all deer in the forest, what is the best estimate of the number of deer in the park?
 
Re: i need help i dont know how this all works though

Hello, willmon13!

Edit: Sorry, everyone . . . I have to correct my blunders . . . *blush*

A regional forestry division wanted to estimate the number of deer in a particular national park.
They caught and tagged 70 deer and released them back into the park.
Later they selected a sample of 450 deer. Of the 450 deer, 25 were tagged.

Assuming that the proportion of tagged deer in the sample holds for all deer in the forest,
what is the best estimate of the number of deer in the park?

\(\displaystyle \text{Let }x\text{ = number of deer in the park.}\)

\(\displaystyle \text{Assuming the proportions are the same: }\:\frac{25}{450} \;=\;\frac{70}{x}\)

\(\displaystyle \text{We have: }\:25x \:=\:31500 \quad\Rightarrow\quad x \:=\:1260\)


. . There are approximately 1260 deer in the park.

 
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