game wardens use experiments to help determine the number of deer in the state of North Carolina. Suppose 100 deer are caught, tagged, and released back into the wild. A month later 800 deer are caught with 16 found to have tags. Using this information, estimate the number of deer in North Carolina.
We can use the proportion of tagged deer to estimate the total number of deer in North Carolina:
100 tagged / unknown total population = 16 tagged / 800 caught
Simplifying this equation, we can cross-multiply to get:
100 tagged x 800 caught = 16 tagged x unknown total population
Dividing both sides by 16 tagged, we get:
100 tagged x 800 caught / 16 tagged = unknown total population
Simplifying this expression, we get:
5000 = unknown total population
Therefore, we can estimate that there are approximately 5000 deer in North Carolina.
To estimate the number of deer in North Carolina, we can set up a proportion using the number of tagged deer caught in the second experiment and the total number of deer caught in both experiments.
Let "x" represent the total number of deer in North Carolina.
From the information provided, we know that:
- In the first experiment, 100 deer were caught, tagged, and released.
- In the second experiment, 800 deer were caught, with 16 having tags.
Therefore, we can write the proportion:
(16 tagged deer / 800 total deer) = (100 tagged deer / x total deer)
To solve for "x," we can cross-multiply and then divide:
16x = 100 * 800
16x = 80,000
x = 80,000 / 16
x = 5,000
Based on this estimate, there are approximately 5,000 deer in North Carolina.
To estimate the number of deer in North Carolina using the given information, we can use a method called "mark and recapture" or "capture-recapture."
1. The mark and recapture method assumes that the ratio of tagged deer to total deer in the second sample is representative of the entire population. Based on this assumption, we can set up a proportion to estimate the population size.
2. Let's assign variables:
- N: Total population size (the number we are trying to estimate)
- n1: Number of deer caught and tagged in the first sample
- n2: Number of deer caught in the second sample
- x: Number of deer with tags found in the second sample
3. Given data:
- n1 = 100 (number of deer tagged initially)
- n2 = 800 (total number of deer caught in the second sample)
- x = 16 (number of tagged deer found in the second sample)
4. Now let's set up the proportion:
n1/N = x/n2
Plugging in the values we have:
100/N = 16/800
5. Cross-multiply and solve for N:
(100 x 800) = (16 x N)
80,000 = 16N
N = 80,000 / 16
N ≈ 5,000
Therefore, based on this estimation method, the number of deer in North Carolina is estimated to be around 5,000.