Santiago, a park ranger, was trying to estimate the number of catfish in a lake. He randomly caught 32 catfish, tagged them, and let them go.
Six months later, he surveyed fisherman at the lake about how many catfish they caught that were tagged. His survey results showed that 350 catfish were caught and 13 had tags on them.
Which is the best estimate for the size of the catfish population in the lake?
(32/13)*350 = 862
To estimate the size of the catfish population in the lake, we can use a method called mark and recapture.
In this method, we assume that the ratio of tagged catfish in the first sample to the total population is approximately equal to the ratio of tagged catfish in the second sample to the estimated population size.
Let's calculate the estimated population size using this formula:
Estimated Population Size = (Number of tagged catfish in the first sample) * (Total population size) / (Number of tagged catfish in the second sample)
In this case:
Number of tagged catfish in the first sample = 32
Total population size = unknown (the size we want to estimate)
Number of tagged catfish in the second sample = 13
Applying the formula:
Estimated Population Size = (32) * (Total population size) / (13)
To find the estimated population size, we can rearrange the formula:
Total population size = (Estimated Population Size) * (Number of tagged catfish in the second sample) / (Number of tagged catfish in the first sample)
Plugging in the numbers:
Total population size = (32) * (350) / (13)
Total population size ≈ 864
Therefore, the best estimate for the size of the catfish population in the lake is approximately 864.