How Accurate is the Fish Population Estimate in the Lake?

[Alexsandro]

Researchers of a department of engineering of fish are studying the fish of a lake. In the first phase of the work they collect 100 fish, place labels in all they and they return them to the lake. One week later them they come back to the lake, they collect more 100 fish and they observe that 7 of them possesses labels.

(a) Which the best estimate for the number of fish in the lake?

(b) That assumptions must be satisfied to justify the estimate of the previous item ?

 

[mathman]

(a) N=100(100/7)=1428

(b) Extrapolation - since 7/100 of the caught fish were tagged, assume that 7/100 times (N) total number of fish = total number of that have been tagged (=100).