Calculate Wheat Field Yields: Mean of 10 Tons/Acre with 2 SD - Practice Problem

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Discussion Overview

The discussion revolves around calculating the expected number of wheat fields yielding between 8 to 12 tons per acre, based on a sample mean of 10 tons/acre and a standard deviation of 2 tons. Participants are exploring the application of the normal distribution to this problem.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant states that they hope the answer is 68, expressing confusion about when to use the percentages associated with 1 and 2 standard deviations.
  • Another participant clarifies that 68.3% represents the area under the normal curve within 1 standard deviation, while 95.4% corresponds to 2 standard deviations, suggesting that the correct answer for the 8 to 12 ton range is indeed 68 fields.
  • A further comment indicates that if the range were adjusted to 6 to 14 tons, then 95 fields would be the expected count based on the 2 standard deviation rule.

Areas of Agreement / Disagreement

Participants express differing views on the correct application of standard deviation percentages, with some agreeing on the use of 68.3% for the 8 to 12 ton range, while others note that a different range would yield a different expected count.

Contextual Notes

The discussion does not resolve the confusion regarding the application of standard deviation percentages, and assumptions about the normality of the data are not explicitly stated.

taffyleg
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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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What have you figured out so far?
 
I'm hoping the answer is 68. I don't understand at what point you differentiate between multiplying by 95.4% or 68.3%.
 
taffyleg said:
I'm hoping the answer is 68. I don't understand at what point you differentiate between multiplying by 95.4% or 68.3%.

68.3% the the area under the normal curve within 1 standard deviation; 95.4% is the area under the normal curve within 2 standard deviations.

Since the question gives you 1 standard deviation in either direction, your answer is correct. 95 fields would be the correct answer if they asked for the numbr with 6 to 14 tons.
 

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