While doing research on a lake, biologists tagged 200 walleye. Later, they captured 160 walleye, of which 16 had tags. What is the BEST estimate for the walleye population?
Responses
A 2,6002,600
B 3,0003,000
C 2,0002,000
D 2,300
The BEST estimate for the walleye population would be:
(200 tagged walleye / proportion of tagged walleye in second sample)
proportion of tagged walleye in second sample = (16 tagged walleye / 160 total walleye in second sample) = 0.1
So, the estimate would be:
(200 tagged walleye / 0.1) = 2,000
Therefore, the answer is C) 2,000.
To estimate the walleye population, we can use a proportion based on the ratio of tagged walleye to the total captured walleye.
The proportion can be set up as:
(tagged walleye / total captured walleye) = (total tagged walleye / total walleye population)
Now we can substitute the given information into the proportion:
16 / 160 = 200 / x
To solve for x (the total walleye population), we can cross-multiply:
16x = 160 * 200
16x = 32,000
Divide both sides by 16:
x = 2,000
Therefore, the best estimate for the walleye population is 2,000.
The correct answer is C) 2,000.
To estimate the walleye population, we can use the mark and recapture method. In this method, we assume that the proportion of tagged walleye in the second sample is representative of the proportion of tagged walleye in the entire population.
First, we calculate the proportion of tagged walleye in the second sample. We divide the number of tagged walleye in the second sample (16) by the total number of walleye in the second sample (160): 16/160 = 0.1.
Next, we use this proportion to estimate the total walleye population. We divide the number of tagged walleye in the first sample (200) by the proportion of tagged walleye in the second sample (0.1): 200/0.1 = 2000.
Therefore, the best estimate for the walleye population is 2,000.
The correct answer is C (2,000).