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In order to estimate the population size of a fish species in a lake, a researcher captures 100 fish from the lake and marks them with coloured tags. A week later, the researcher returns to the lake and catches 150 fish of the same species and finds that 25 of them are previously tagged ones. Assuming no immigration or emigration occurred, the total population size of the fish species in the lake will be
17
38
600
860
Answers (1)
To estimate the total population size of the fish species in the lake, we can use the mark and recapture method. In this case, the researcher marked 100 fish initially and then caught 150 fish during the second sampling, finding 25 of them to be previously tagged.
The mark and recapture method is based on the assumption that the ratio of marked to total population in the first sample is equal to the ratio of marked to total population in the second sample. Using this assumption, we can set up the following proportion:
(Initial marked fish / Total population) = (Recaptured marked fish / Second sample size)
Let's plug in the given values:
(100 / Total population) = (25 / 150)
To solve for the total population size, we can cross-multiply and solve the equation:
25 * Total population = 100 * 150
Total population = (100 * 150) / 25
Total population = 600
Therefore, the estimated total population size of the fish species in the lake is 600 that is option 3.
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