many bird species on the pitcairn islands are in decline. in order to estimate the population of a…

many bird species on the pitcairn islands are in decline. in order to estimate the population of a particular species of bird, scientists mark 168 birds by attaching very small computer chips to them. a few days later, the scientists catch 495 birds, 66 of which are marked with computer chips. to the nearest whole number, what is the best estimate for the bird population?

many bird species on the pitcairn islands are in decline. in order to estimate the population of a particular species of bird, scientists mark 168 birds by attaching very small computer chips to them. a few days later, the scientists catch 495 birds, 66 of which are marked with computer chips. to the nearest whole number, what is the best estimate for the bird population?

Answer

Explanation:

Step1: Set up the proportion

Let $x$ be the total population of the bird species. The proportion of marked - birds in the first sample to the total population is equal to the proportion of marked - birds in the second sample to the size of the second sample. So, $\frac{168}{x}=\frac{66}{495}$.

Step2: Cross - multiply

Cross - multiplying gives us $66x = 168\times495$.

Step3: Calculate the right - hand side

$168\times495=168\times(500 - 5)=168\times500-168\times5=84000 - 840 = 83160$. So, $66x = 83160$.

Step4: Solve for $x$

$x=\frac{83160}{66}=1260$.

Answer:

1260