Optimizing Subgroup Selection in Gaussian Distribution for Error Analysis

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Homework Help Overview

The discussion revolves around a problem from an error analysis course involving Gaussian distributions of resistor values. The original poster seeks to form a subgroup of resistors with specific statistical properties from a larger set characterized by a Gaussian distribution.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to determine the value of 'a' needed to achieve a subgroup with a mean of 100 ohms and a standard deviation of 5 ohms. Some participants reference statistical principles related to sampling from a normal distribution, while others express confusion about the implications of the problem's parameters, particularly the lack of information on sample size.

Discussion Status

Participants are exploring various interpretations of the problem, with some suggesting relevant statistical concepts. However, there is no explicit consensus on how to proceed, and the original poster expresses ongoing confusion about the problem's requirements.

Contextual Notes

There is a noted absence of information regarding the number of samples, which may impact the analysis. The original poster also indicates a time constraint for resolving the problem.

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?
 
Last edited:
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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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