# Thread: Difference between two normal distributions

1. ## Difference between two normal distributions

I have two normal distributions, with different means but the same variance. How can I find the probability for that the difference between a sample taken from each distribution is above x? Not sure how to approach this. Would appreciate any help.

2. Originally Posted by gralla55
I have two normal distributions, with different means but the same variance. How can I find the probability for that the difference between a sample taken from each distribution is above x? Not sure how to approach this. Would appreciate any help.
Read this: Normal Difference Distribution -- from Wolfram MathWorld

3. $\displaystyle P(\bar X-\bar Y>a)=P\left( {(\bar X-\bar Y)-(\mu_X-\mu_Y)\over \sqrt{ {\sigma^2\over n} + {\sigma^2\over m}}}>{a-(\mu_X-\mu_Y)\over \sqrt{ {\sigma^2\over n} + {\sigma^2\over m}}}\right)$

$\displaystyle =P\left( Z>{a-(\mu_X-\mu_Y)\over \sqrt{ {\sigma^2\over n} + {\sigma^2\over m}}}\right)$