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 3,0003,000
B 2,6002,600
C 2,3002,300
D 2,000
AAAaannndd the bot gets it wrong yet again!
16/160 = 200/x
x=2000
My apologies for the mistake, you are correct! The correct calculation would be:
16/160 = 200/x
Cross multiplying:
16x = 200 * 160
16x = 32,000
x = 2,000
Therefore, the best estimate for the walleye population is 2,000.
To find the best estimate for the walleye population, we can use the capture-recapture method. This method assumes that the proportion of tagged individuals in the first sample is approximately equal to the proportion of tagged individuals in the overall population.
First, let's set up a proportion based on the capture-recapture method:
(Number of tagged individuals in the first sample) / (Total number of individuals in the first sample) = (Number of tagged individuals in the second sample) / (Estimated total population)
Given information:
Number of tagged individuals in the first sample = 200
Total number of individuals in the first sample = 160
Number of tagged individuals in the second sample = 16
Now we can plug in the values and solve for the estimated total population:
(200 / 160) = (16 / Estimated total population)
To solve for Estimated total population, we can cross-multiply:
200 * Estimated total population = 16 * 160
Dividing both sides by 200:
Estimated total population = (16 * 160) / 200
Estimated total population = 12.8
Since you cannot have a fraction of a walleye, the best estimate for the walleye population is rounded to the nearest whole number.
Therefore, the BEST estimate for the walleye population is 13.
None of the given answer choices match the best estimate (13), so none of the options provided is correct.
Option B: 2,600.
This is found by setting up a proportion:
tagged walleye in sample / total sample = tagged walleye in population / total population
Plugging in the given numbers:
16/160 = 200/x
Solving for x (the total population):
16x = 200 * 160
x = 2,600.