I recently watched a documentary on Mathematics. In the show they managed to estimate the weight of the largest fish that the fisherman was likely to of ever caught in his career just by analysing one day's catch.
The presenter states he used the Normal Distribution Equation to figure this out. Could someone elaborate on how they managed to estimate the largest fish the fisherman ever caught by analysing just a few fish?
Details
Here are the steps they used to estimate the weight of the largest fish likely to of ever been caught in the fisherman's career.
A fisherman caught some fish.
The fish were weighed.
Then, the average weight of the fish were calculated
Then, the Standard deviation was calculated
Then, the total amount of fish caught in the fisherman's career was calculated
- 40 years * 8 weeks during the year = 320
- 320 * 6 days of the week = 1920
- 1920 * 200 fish per day = 384,000 fish caught in his whole career.
Using these numbers he calculated the largest out of the 384,000 should be 1.3 KG, which turned out to be correct. How did he achieve this using Normal Distribution? The video is a little bare on the details being aimed at the layman.
Best Answer
If you look up the standard score table, $0.13\%=0.0013 \approx \frac 1{800}$ of the events are above mean+$3\sigma$ and most of those are close to mean+$3\sigma$. Based on that, if he had caught $800$ fish, you would predict tat the largest was about mean+$3\sigma$. They did the same thing based on the larger quantity of fish. Out of $384,000$ fish you would expect the largest to be about $4.556 \sigma$ high. This depends sensitively on the assumption that fish sizes are distributed normally, which is probably not true.