Confidence of Distribution

Hi all,
say I have a known normal distribution, which was created by an experiment. Now, I take another measurement, one only, and assume this is the mean of my new distribution, with similar properties as the known distribution. How can I calculate, how sure I am that this new distribution is within a certain limit to my known normal distribution from my experiment?

I would really appreciate any help on this matter.
Thank you


Less is more. Stay pure. Stay poor.
Yeah, a little confusing. Take a look at two sample Kolmogov-Shapiro test (I may have misspelled the first name) to see if that is what you are getting at.