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To estimate the number of catfish present in the lake, you can use the proportion of catfish in the sample to the total number of fish in the sample.
First, calculate the proportion of catfish in the sample:
Proportion of catfish = Number of catfish / Total number of fish in the sample
Proportion of catfish = 52 / (52 + 61 + 87) = 52 / 200 = 0.26
Next, apply the proportion to the total number of fish in the lake:
Estimated number of catfish = Proportion of catfish * Total number of fish in the lake
Estimated number of catfish = 0.26 * 800 = 208
Therefore, an estimated 208 catfish are present in the lake if a sample of 800 fish is collected.