Question

an ornithologist who specializes in seagulls decides to estimate the seagull population in his local area. to do so, he traps 26 seagulls and marks them. after releasing the seagulls and waiting a bit, he traps 190 seagulls and observes that 13 of them are marked. to the nearest whole number, what is the best estimate for the seagull population?

Explanation:

Step1: Set up proportion

Let \( N \) be the total population. The proportion of marked seagulls in the second sample should equal the proportion of marked seagulls in the total population. So, \(\frac{\text{marked in first sample}}{\text{total population}}=\frac{\text{marked in second sample}}{\text{second sample size}}\), which is \(\frac{26}{N}=\frac{13}{190}\).

Step2: Solve for \( N \)

Cross - multiply: \( 13N = 26\times190 \). Then, \( N=\frac{26\times190}{13} \). Simplify \( 26\div13 = 2 \), so \( N = 2\times190=380 \).

Answer:

380