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 6,2006,200
B 6,4006,400
C 6,6006,600
D 6,800
6,800
why
This is because the researchers marked 340 trout and later found 30 trout with tags out of 600 that were captured. We can set up a proportion:
340/x = 30/600
Cross-multiplying, we get:
30x = 20400
Dividing by 30 on both sides:
x = 680
Therefore, the best estimate for the trout population is 6800 (340 marked trout multiplied by 20). Thus, the answer is D) 6,800.
To find the best estimate for the trout population, we can use a proportion based on the number of tagged trout.
We know that 340 trout were tagged out of the total population. We can set up the proportion:
tagged trout / total trout = tagged trout in sample / total trout in sample
We can fill in the values we know:
340 / total trout = 30 / 600
To solve for the total trout, we can cross-multiply and solve for the unknown:
(340 * 600) / 30 = total trout
20 * 600 = total trout
12000 = total trout
Therefore, the best estimate for the trout population is 12,000.
None of the given options match the best estimate of 12,000.