If you put 200 tagged fish in a pond, then collect a sample of 50 and 8 of them are tagged. How many fish are in the pond?
8 is 16% of the 50 sampled.
That means that 200 is 16% of the whole population.
0.16p = 200
...
40 out of 72 fish in one lake were tagged by a wildlife researcher. At a second lake, 260 fish were tagged. If fish were tagged at proportional rates in the two lakes, how many fish were in the second lake?
To calculate the estimated number of fish in the pond, we can use a proportion based on the ratio of tagged fish in the sample to the total number of fish in the pond.
Let's say the total number of fish in the pond is represented by "N."
We know that out of a sample of 50 fish, 8 are tagged. We can set up the proportion as follows:
(8 tagged fish in the sample) / (50 fish in the sample) = (200 tagged fish in the pond) / N
Now we can cross-multiply and solve for N:
8 / 50 = 200 / N
8N = 50 * 200
8N = 10,000
N = 10,000 / 8
N ≈ 1,250
Therefore, there are approximately 1,250 fish in the pond.
To find the estimated number of fish in the pond, you can use the concept of proportionality. You know that 8 out of the sample of 50 fish are tagged.
Let's set up a proportion to find the total number of fish in the pond:
"Tagged fish in sample" : "Total fish in pond" = "Tagged fish in population" : "Total population"
Using the numbers given, the proportion can be written as:
8 : 50 = 200 : x
To solve for x, you can cross-multiply and then divide:
8 * x = 50 * 200
8x = 10,000
x = 10,000 / 8
x = 1,250
Therefore, based on this estimation, there are approximately 1,250 fish in the pond.