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