Question

for a research study on various types of lizards, scientists wanted to estimate the local skink population. they captured, marked, and released 105 skinks. a week later, the scientists returned to the site and found 14 marked skinks out of the 376 skinks they counted. to the nearest whole number, what is the best estimate for the skink population?

Explanation:

Step1: Set up proportion

Let \( N \) be the total population. The proportion of marked skinks in the first sample (marked and released) to the total population should be equal to the proportion of marked skinks in the second sample (recaptured) to the number of skinks in the second sample. So we have the proportion: \(\frac{105}{N}=\frac{14}{376}\)

Step2: Solve for \( N \)

Cross - multiply to get \( 14N = 105\times376\). First, calculate \( 105\times376 = 105\times(300 + 70+6)=105\times300+105\times70 + 105\times6=31500+7350+630 = 39480\). Then, solve for \( N \) by dividing both sides of the equation \( 14N = 39480\) by 14: \( N=\frac{39480}{14}\approx2820\)

Answer:

2820