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

[taffyleg]

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.

 

[CRGreathouse]

What have you figured out so far?

 

[taffyleg]

I'm hoping the answer is 68. I don't understand at what point you differentiate betwen multiplying by 95.4% or 68.3%.

 

[CRGreathouse]

I'm hoping the answer is 68. I don't understand at what point you differentiate betwen 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.