Optimizing Subgroup Selection in Gaussian Distribution for Error Analysis

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SUMMARY

This discussion focuses on optimizing subgroup selection from a Gaussian distribution of resistors for error analysis. The resistors have a mean resistance (μ) of 100 ohms and a standard deviation (σ) of 20 ohms. The goal is to form a subgroup with a mean of 100 ohms and a standard deviation of 5 ohms by determining the limits (r1 and r2) based on a value 'a'. Participants highlight the need to understand the error function and the implications of sampling from a normal distribution, particularly regarding variance and sample size.

PREREQUISITES
  • Understanding of Gaussian distribution properties
  • Knowledge of standard deviation and mean calculations
  • Familiarity with the error function in statistics
  • Basic concepts of sampling and variance in statistics
NEXT STEPS
  • Study the error function and its applications in Gaussian distributions
  • Learn about sampling distributions and their impact on mean and variance
  • Explore the Central Limit Theorem and its relevance to subgroup selection
  • Investigate statistical software tools for performing Gaussian analysis
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Statisticians, data analysts, and students in error analysis or probability courses who are working with Gaussian distributions and subgroup selection methods.

mpm166
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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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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.
 
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
 
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.
 

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