Calculating Wheat Field Yield Variance: A Quick Statistics Problem

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The discussion focuses on calculating the expected number of wheat fields yielding between 8 to 12 tons per acre, given a mean yield of 10 tons and a standard deviation of 2. Participants are prompted to show their work in determining the standard normal variable and using a normal probability distribution table. The importance of demonstrating calculations is emphasized, as it aids in understanding the statistical process. A resource for a normal probability distribution table is provided for those who need it. Clear calculations are essential for accurately estimating yield variance in agricultural statistics.
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For a sample of 100 wheat fields, the mean yield was 10 tons/acre and the standard deviation 2. Approximately how many fields out of the 100 should have yields in the 8 to 12 ton range? Show work.
 
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But you haven't (shown your work, that is). What have you done on this? Do you know how to find the standard normal variable? Do you have a table of the normal probability distribution? If not, here's a good one on line:
http://people.hofstra.edu/Faculty/Stefan_Waner/RealWorld/normaltable.html
 
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I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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