Optimizing Subgroup Selection in Gaussian Distribution for Error Analysis

In summary, the question asks for a method to determine a value for a given resistor within a given subgroup of resistors with a certain range of resistors with a certain mean and standard deviation. The problem does not provide enough information to proceed.
  • #1
mpm166
14
0
Here is a question I can not seem to get from an error analysis course.

Assume that you have a box of resistors that have a gaussian distribution of resisances with mean value mu=100 ohm and standard deviation sigma=20 ohm (20%resistors). Suppose that you wish to form a subgroup of resistors with mu= 100ohm and standard deviation of 5ohm (ie. 5%resistors) by selecting all resistors with resistance between the two limits r1= mu -a, and r2 = mu + a.
a) find the value of a
b) what fraction of the resistors should satisfy the condition?
c) Find the standard deviation of the remaining sample.

My problem is finding the value of a. At first glance I thought it would simply be 5, but after some thought it would appear that its more complicated than this because your taking from a sample. Also, I was not sure whether the new subgroup would follow a gaussian distribution. I'm having some troubles wrapping my head around this one.

Can anyone help me get started?
 
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  • #2
Hi,
I had a probability/stats class where we studied similar stuff. We had a corollary that says if you take a sample from a normal(gaussian) distribution with mean mu and variance sigma^2, then the sample has a normal distribution with mean mu and variance sigma^2/n. It's been awhile since I studied that stuff. Hope this helps.
 
  • #3
hmmm, the only thing is, the problem gives no indication of the number of samples. it would appear that we have to look at the error function (integral of the gaussian distribution), but I'm still not sure what exactly is necessary.

to be honest, everytime I think about this problem I seem to confuse myself more (it just seems to be over my head, playing with these distributions). if someone could clarify a general approach to the problem that would be great cause I'm still very confused
 
  • #4
any chance at a little help, I've done the rest of the problems but I really need to figure this one out by tomorrow.

any help is greatly appreciated.
 

FAQ: Optimizing Subgroup Selection in Gaussian Distribution for Error Analysis

1. What is error analysis and why is it important?

Error analysis is a method used in scientific research to identify and quantify the uncertainties and mistakes in experimental data. It is important because it allows researchers to evaluate the reliability and accuracy of their data, and to make adjustments or improvements to their methods if necessary.

2. How is error analysis performed?

Error analysis involves identifying potential sources of error in an experiment, estimating their impact on the data, and calculating the total error using statistical methods. This can include analyzing the precision and accuracy of instruments, human error, and environmental factors.

3. What is the difference between systematic and random errors?

Systematic errors are consistent and reproducible deviations from the true value of a measurement, and can be caused by faulty equipment or flawed experimental design. Random errors are unpredictable fluctuations in data caused by factors such as variations in environmental conditions or human error.

4. How can error analysis help improve the validity of experimental results?

By identifying and quantifying sources of error, error analysis can help researchers make adjustments to their methods or equipment to improve the reliability and accuracy of their data. This can lead to more valid and meaningful results.

5. Are there any limitations to error analysis?

While error analysis is a valuable tool in scientific research, it does have limitations. It cannot account for all possible sources of error and may not be able to accurately quantify certain types of errors. Additionally, error analysis is based on assumptions and may not be applicable in all experimental situations.

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