SOLUTION: To determine the number of deer in a game reserve, a forest ranger catchers 127 deer, tags them and releases them. Later 189 deer are caught and it is found that 82 of them are tag

Algebra ->  Probability-and-statistics -> SOLUTION: To determine the number of deer in a game reserve, a forest ranger catchers 127 deer, tags them and releases them. Later 189 deer are caught and it is found that 82 of them are tag      Log On


   

Question 476235: To determine the number of deer in a game reserve, a forest ranger catchers 127 deer, tags them and releases them. Later 189 deer are caught and it is found that 82 of them are tagged. Estimate how many deer are in the game reserve and round the answer to the nearest interger. I got 293 but I don't think it's right, please assist.
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
The assumption is that the 189 deer represent a random sample of the entire reserve so the proportion of tagged deer in the sample will represent the proportion of tagged deer in the reserve.
The proportion for sample is 82%2F189
The proportion for reserve is 127%2Fx
where x is the estimate of deer in entire reserve
set them equal to each other
82%2F189+=+127%2Fx
Multiply by x on both sides
%2882%2F189%29%2Ax+=+127
Multiply by reciprocal of left side
%28189%2F82%29%2882%2F189%29%2Ax+=+127%2A%28189%2F82%29
x+=+%28127%2A189%29%2F82
x+=+292.72
Therefore, you are correct there is about 293 deer.