Chebyshev's Theorem: Decision for Lumber Buyer

[moor]

1.

A buyer for a lumber company must decide whether to buy a piece of land containing 5,000 pine trees. If 1,000 of the trees are at least 40 feet tall, the buyer will purchase the land; otherwise, he won't. The owner of the land reports that the height of the trees has a mean of 30 feet and a standard deviation of 3 feet. Based on this information, what is the buyer's decision?

Homework Equations

By Chebyshev’s Theorem (1-1/K2 )

The Attempt at a Solution

By Chebyshev’s Theorem (1-1/K2 )
1000/5000= 1/5 = 1-1/K2 so
1/K2 = 1-1/5 = 4/5 so

K = 1.118, so

20% fall between 26.646 and 33.354


So I advise against .

Is this right?

 

[jbsteele]

The buyer should not purchase the land because there is only a 20% chance that at least 1,000 of the trees are 40 feet tall.

 

[tomcue]

I would suggest that the buyer use Chebyshev's Theorem as a guideline, but also consider other factors such as the cost of the land and potential profits from the trees. Chebyshev's Theorem gives a general estimate of the proportion of trees that are at least 40 feet tall, but it does not take into account potential outliers or other factors that may affect the decision. It would be beneficial for the buyer to conduct further research and analysis before making a final decision.