Lets assume I have a origin distribution, lets call it Omega, which is heavily skewed and does not seem to be normally distributed.
I now apply a log(n+1) function to it and get a normal distribution with little to no skew, lets call it Beta.
My question is: When I calculate confidence intervals for Beta, can I say something like "Point number 312 in Beta lies within the 95% confidence interval, so it can be said that point 312 in Omega also lies within a 95% confidence interval!"?
Can I assume Omega is normally distributed, because a transformation of the distribution is?
If I can not make those assumptions, which assumptions can be made about Omega which show in Beta and its confidence intervals?
Sorry probably these are very basic questions, but I often fail to grasp the meaning of very mathematical topics which are often described in a very formal way.
Best regards