Pecan trees drop an organic compound called juglone that inhibits growth of new trees and many...

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Pecan trees drop an organic compound called juglone that inhibits growth of new trees and many other plants. This naturally controls overcrowding. A pecan farmer is interested in the distance from any healthy mature pecan tree to the next closest tree. Planting trees too close together compromises pecan production, while planting trees too far apart sacrifices potential income. If he hopes to have 80% of the trees grow to healthy maturity, how far apart should he plant them? Assume the distribution of distances follows an approximately uniform distribution of 40-60 feet. Pecan trees drop an organic compound called juglone that inhibits growth of new trees and many other plants. This naturally controls overcrowding. A pecan farmer is interested in the distance from any healthy mature pecan tree to the next closest tree. Planting trees too close together compromises pecan production, while planting trees too far apart sacrifices potential income. If he hopes to have 80% of the trees grow to healthy maturity, how far apart should he plant them? Assume the distribution of distances follows an approximately uniform distribution of 40-60 feet.

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