I am a bit confused when it comes to 68-95-99.7 rule of confidence interval of normal distribution. Normally I could see confidence interval of 95% for a sample statistic (s) with margin of error lets say e. So the confidence interval is s +- e. So 95% means that if we do the sampling 100 times and calculate the sample statistic s 100 times then for each we will have different s+-e. However 95 times the true population parameter p lies within s+-e.
This is what I have understood about confidence interval. The confidence interval is s+-e and the confidence level is 95%.
Now when it comes to normal distribution, how the above idea fits in. I mean here confidence interval is mui+-sigma and the confidence level is 68%?. According to wikipedia it is something like this
About 68% of values drawn from a normal distribution are within one standard deviation σ away from the mean; about 95% of the values lie within two standard deviations; and about 99.7% are within three standard deviations
I am confused where is the sample statistic here, it says the values drawn(which is directly the random variable).