Question

Biologists tagged 166 fish in a lake on January 1. On February 1, they returned and collected a random sample of 33 fish, 11 of which had been previously tagged. On the basis of this experiment, approximately how many fish does the lake have?

Answer 1

The estimated fish population in the lake is about 45 fish.

Step-by-step explanation:

The student wants to estimate the total number of fish in a lake based on a mark and recapture experiment. In the experiment, biologists tagged 166 fish on January 1 and collected a random sample of 33 fish on February 1, 11 of which had been previously tagged. This method assumes that the larger the population, the lower the percentage of tagged organisms that will be recaptured since they will have mixed with more untagged individuals. By using the mark and recapture equation, we can estimate the population size:

N = (M x C) / R

where N is the population size, M is the total number of fish tagged initially, C is the total number of fish caught in the second round, and R is the number of recaptured tagged fish. Plugging in the values for this experiment, we have:

N = (166 x 33) / 11 = 498 / 11 = 45

Therefore, the estimated fish population in the lake is about 45 fish.

Answer 2

The estimated size of the lemur population can be determined using the mark and recapture method. In this case, 37 lemurs were initially captured and marked, and 49 lemurs were later captured, of which 11 were previously marked. Using the formula (Number of tagged individuals in first sample) x (Total number of individuals in second sample) / (Number of recaptured tagged individuals in second sample) = Estimated population size, the population size is calculated to be 167.

Step-by-step explanation:

The estimated size of the lemur population can be determined using the mark and recapture method. In this case, 37 lemurs were initially captured and marked, and 49 lemurs were later captured, of which 11 were previously marked. To estimate the population size, we can use the formula: (Number of tagged individuals in first sample) x (Total number of individuals in second sample) / (Number of recaptured tagged individuals in second sample) = Estimated population size. Plugging in the values, we have: (37 x 49) / 11 = 167. Therefore, the estimated size of the lemur population is 167 individuals.