A group of researchers wanted to monitor the trout population, so they marked 340 trout with tags. Later, they captured 600 trout and found that 30 of them had tags. What is the BEST estimate for the trout population?

Question

A group of researchers wanted to monitor the trout population, so they marked 340 trout with tags. Later, they captured 600 trout and found that 30 of them had tags. What is the BEST estimate for the trout population?

Responses

A 6,200

B 6,800

C 6,400

D 6,600

Answer 1

We can set up a proportion:

340 (number of tagged trout) is to x (total population) as 30 (number of tagged trout in the sample) is to 600 (total sample size).

Using cross-multiplication, we get:

340x = 30 * 600

Simplifying the right side:

30 * 600 = 18000

Dividing both sides by 340:

x = 18000/340

x ≈ 52.94

So the best estimate for the trout population is about 52,900. However, none of the answer choices are close to this estimate, so we need to round to the nearest thousand.

52,900 rounded to the nearest thousand is 53,000, which is closest to option D, 6,600. So the answer is D.