Question

scientists captured, tagged, and released 20 crows as part of a research study. a week later, they counted 250 crows, of which 10 had tags. to the nearest whole number, what is the best estimate for the crow population?

Explanation:

Step1: Set up proportion

Let \( N \) be the total population. The proportion of tagged crows in the second sample should be equal to the proportion of tagged crows in the total population. So \(\frac{\text{tagged in first sample}}{\text{total population}}=\frac{\text{tagged in second sample}}{\text{second sample size}}\), which is \(\frac{20}{N}=\frac{10}{250}\).

Step2: Solve for \( N \)

Cross - multiply: \( 10N = 20\times250 \). Then \( 10N=5000 \). Divide both sides by 10: \( N=\frac{5000}{10}=500 \).

Answer:

500