To determine the number of fish in a lake , a conservationist catches 500 fish, tags them, and releases them into the lake. Later, 120 fish are caught and 25 of them are tagged. Estimate the number of fish in the lake.
since 25 is 21% of 120, then assuming that the 500 tagged fish have dispersed evenly into the fish population, 500 is 21% of the whole population.
So, 500/.21 = 2400 is a good estimate of the whole population
To estimate the number of fish in the lake, we can use a method called mark and recapture. In this method, we assume that the proportion of tagged fish in the second sample is equal to the proportion of tagged fish in the entire population.
Let's denote:
- N = total number of fish in the lake (what we want to estimate)
- n1 = number of fish caught and tagged in the first sample = 500
- n2 = number of fish caught in the second sample = 120
- x = number of tagged fish caught in the second sample = 25
Now, we can set up a proportion:
(n1/N) = (x/n2)
Plugging in the known values, we have:
(500/N) = (25/120)
To solve this equation for N, we can cross-multiply and solve for N:
500 * 120 = 25 * N
60,000 = 25N
Dividing both sides of the equation by 25, we get:
N = 2,400
Therefore, the estimated number of fish in the lake is 2,400.