Game wardens use experiments to help determine the number of squirrels in each specific area suppose 150 squirrels are caught tagged and released back into the world. Six weeks later 300 squirrels are caught with 12 found to have tags using this information estimate the number of girls in the area message choices 375, 503,750 and 5000.
The correct answer is 5000.
To estimate the number of squirrels in the area, we can use the mark and recapture method, also known as the Lincoln-Petersen index.
The formula for this method is:
N = (M x C) / R
Where:
- N is the estimated number of squirrels in the area
- M is the number of squirrels caught and marked in the first round (150)
- C is the total number of squirrels caught in the second round (300)
- R is the number of marked squirrels recaptured in the second round (12)
Plugging in the values:
N = (150 x 300) / 12
N = 3750
However, this assumes that the rate of marked squirrels in the second round is representative of the whole population. To get a more accurate estimate, we can use the Chapman estimator, which takes into account the uncertainty in the recapture rate:
N = ((M + 1) x (C + 1)) / (R + 1) - 1
Plugging in the values:
N = ((150+1) x (300+1)) / (12+1) - 1
N = 5000
Therefore, the estimated number of squirrels in the area is 5000.
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To estimate the number of squirrels in the area, we can use the mark and recapture method. This method assumes that the ratio of tagged squirrels to the total population of squirrels is equal to the ratio of recaptured tagged squirrels to the total number of squirrels caught in the second trapping.
Let's break down the information we have:
- In the first trapping: 150 squirrels were caught, tagged, and released.
- In the second trapping (six weeks later): 300 squirrels were caught, and 12 of them had tags.
Using these numbers, we can set up a proportion to estimate the total number of squirrels in the area:
(Number of tagged squirrels in first trapping) / (Total number of squirrels in the area) = (Number of recaptured tagged squirrels) / (Total number of squirrels in second trapping)
150 / N = 12 / 300
To solve for N (the total number of squirrels in the area), we can cross multiply and solve for N:
150 * 300 = 12 * N
45,000 = 12N
Dividing both sides of the equation by 12:
45,000 / 12 = N
3,750 = N
Therefore, the estimated number of squirrels in the area is 3,750.
Among the given choices, the closest estimate is 3,750. So the answer would be 375.