In order to estimate the bear population in the woods, a scientist tags 16 bears. The next week, he observes 240 bears and 8 of them have the tags. Using this ratio, what is the best estimate for the total number of bears in the woods?

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10-04-2024
Mathematics

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In order to estimate the bear population in the woods, a scientist tags 16 bears. The next week, he observes 240 bears and 8 of them have the tags. Using this ratio, what is the best estimate for the total number of bears in the woods?

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maymayisadayday123 maymayisadayday123 · Answer 1 · 2024-04-10T00:56:42+02:00

Answer:

The best estimate for the total number of bears in the woods can be found using the capture-recapture method. This method involves capturing a sample of the population, marking them in some way, and then releasing them back into the population. After some time, another sample is captured, and the number of marked individuals within this sample is counted. The ratio of marked to unmarked individuals in the second sample is used to estimate the total population size.

The formula for estimating the total population size [tex]($N$)[/tex] is given by:

[tex]\[N = \frac{C_1 \times C_2}{M_2}\][/tex]

Where:

- [tex]$C_1$[/tex] is the number of individuals captured and marked in the first sample (16 bears).

- [tex]$C_2$[/tex] is the total number of individuals captured in the second sample (240 bears).

- [tex]$M_2$[/tex] is the number of marked individuals recaptured in the second sample (8 bears).

Let's calculate the estimated total number of bears in the woods.

The best estimate for the total number of bears in the woods, using the capture-recapture method, is 480 bears.

Step-by-step explanation: