Farmer Needs Help!
From: Aik
Guppies are spawned by the hundreds in a fish farm by a farmer. After about 4 weeks, the guppies are ready to be sold on the market. They are weighed before leaving the farm. The average fish weighs 26 grams, but the top 20% weighs an average 41 grams. The farmer is not very good with math, but he wants to calculate and see how the remaining 80% of the distribution looks like:
(1) Average must be 26 grams, (2) Top 20% must average 41 grams, (3) All percentages must add up to 100, (4) Distance between adjacent intervals must be roughly the same, (5) Likely to be roughly bell-shaped distribution (though may be skewed) and with at least 5 intervals.
In another pond, gold fish is being bred. The incubation period is between 3 - 4 weeks. A set of gold fish is ready after 3 weeks weighing 25.5 grams on average, with the remaining weighing an average 29 grams after 4 weeks. The incubation period varies from batch to batch. For one particular batch, 80% was 3-week while 20% was 4-week. The top 20% of the combined 3-week and 4-week gold fish weighs 32 grams on average. Like the above, the farmer is interested to know how the distribution looks like, when there are at least 5 weight intervals. Overall, he wants to know whether it is better for him to breed gold fish or guppy, if the weights of the fish and their distributions (spreads) are the only concerns.
Prizes to be won: $100 of cash prize + $100 of Haagen-Dazs voucher for the 1st prize, $100 voucher for the 2nd prize; and $50 voucher for the 3rd prize. Entries to be received by next Wednesday, 12 April 2006. Judges' decisions will be final, and no petitions will be entertained. Proof of farming knowledge is not necessary, and multiple entries from the same person are encouraged. Query (if any) on the competition to be posted to comments please. Offer is void where prohibited by law. Please send entries, with tables and graphs, to Chelsey bizczc@nus.edu.sg .