A researcher wants to estimate the number of crickets in an isolated valley. They captured 56 crickets in the first session, and then marked and released them. In the second session, they captured 41 crickets of which 8 were already marked.
Assuming that there is no birth, death, immigration, or emigration in the cricket population during the study period, what is the estimated number of crickets in this valley? Match the appropriate population estimate with the data given.
Assuming that there is no birth, death, immigration, or emigration in the cricket population during the study period, what is the estimated number of crickets in this valley? Match the appropriate population estimate with the data given.
Show Hint
- 97
- 247
- 287
- 334
The Correct Option is C
Solution and Explanation
Step 1: Initial capture and marking.
Initially, 56 crickets are captured, marked for identification, and then released back into their habitat to mix with the rest of the population.
Step 2: Second capture.
After a suitable period for the marked crickets to mix with the unmarked population, a second capture session is conducted. In this session, 41 crickets are captured, which includes 8 that had been previously marked.
Step 3: Estimating the total population.
Assuming equal catchability and no changes in the population size due to births, deaths, immigration, or emigration, the population is estimated using the following proportion:
\[ \frac{\text{number of crickets marked in the first catch}}{N} = \frac{\text{number of previously marked crickets recaptured}}{\text{total number of crickets in the second catch}} \] Substituting the values: \[ \frac{56}{N} = \frac{8}{41} \] Solving for \(N\): \[ N = \frac{56 \times 41}{8} = 287 \]
Final Answer: The estimated total number of crickets in the valley is 287.
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