Question

to monitor the population of mule deer, wildlife officials marked 20 mule deer. later, they flew over the area and counted 400 mule deer, of which 10 were marked. to the nearest whole number, what is the best estimate for the mule deer population?

Explanation:

Step1: Set up proportion

Let \( N \) be the total population. The proportion of marked deer in the second sample should equal the proportion of marked deer in the total population. So, \(\frac{\text{marked in total}}{\text{total population}}=\frac{\text{marked in sample}}{\text{sample size}}\), which is \(\frac{20}{N}=\frac{10}{400}\).

Step2: Solve for \( N \)

Cross - multiply: \( 10N = 20\times400 \). Then \( 10N=8000 \). Divide both sides by 10: \( N=\frac{8000}{10}=800 \).

Answer:

800