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# Intersection of two normal distributions2

## Intersection of two normal distributions

(OP)
Hi all,
I am trying to find formulae for calculating the overlap between two normally distributed populations.
There are some online calculators specifically for this but they do not have the resolutinion i require.

So for M1,σ1 and M2,σ2, (where M is Mean and σ is StDev) what formula will give me the probability of samples from these populations overlapping.

Im trying to find the % interferance fit between an OD and ID

I have been using JMP so far as a stop gap but i know this is not entirely accurate, the method below is what im using

by finding the % of Group 2 below the point M1+3(σ1) and vise versa, then multiplying the two %

M+3(σ) still leaves 0.15% of the population unacounted for and i want a more accurate result.

Your comments on a better fast method aswell as the formuala are welcome and appraciated

Thanks

### RE: Intersection of two normal distributions

I think it's a legit question for this forum.  I wasn't aware of the one on Drafting Standards and that doesn't sound like a good fit to me.

I'd be tempted to start with something like a 2 sample t-test with the data.

### RE: Intersection of two normal distributions

The OP's question pertains to "% interferance fit between an OD and ID" which seems to be a tolerancing problem.

### RE: Intersection of two normal distributions

(OP)
While the underlying issue is a tolerance issue, the question and its specifics are statistical, which is why i chose this forum.

So, does anyone have any ideas?

### RE: Intersection of two normal distributions

(OP)
Thanks guys, what i did in the end was create an excel template which will calculate the % overlap of two data sets which can be pasted in.

Much easier than running through differential equations.

The template is giving me almost identical answers to the estimations i made with JMP (identical down to 2 decimals)

It will calculate the overlap between the two points 3 sigma from the mean in each population so there is still a minute % unnacounted for.

The template is attached below if anyone would like to use it.

### RE: Intersection of two normal distributions

(OP)
Sorry, the file attachment function doesnt seem to be working

### RE: Intersection of two normal distributions

((M1-M2)/sqrt(σ1^2+σ2^2))
Paul

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