May I ask is 96% confidence interval and confidence interval of 96th percentile the same? If so, may I ask why?
2026-02-22 23:10:16.1771801816
96% confidence interval and confidence interval of 96th percentile
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No.
A 96% confidence interval is where we think the true value of some statistical measure lie, based on observations. You could say that we are 96% certain that the true value lies inside the confidence interval.
A 96th percentile is the level below which 96% of the data lies, and it is one of those true values I mentioned in the above paragraph (along with mean, standard deviation, and so on). We can estimate where that is based on our data, and we can find a confidence interval, meaning a range of values such that we are pretty certain the true 96th percentile lies within there somewhere. A 5% confidence interval of the 96th percentile is a narrow region around our estimate (we are only 5% certain that the true 96th percentile lies there), while a 90% confidence interval of the 96th percentile is a relatively large region.
To analyze the statement you gave in the comments, there is some true value $x$ such that 96% of the time, the number of active connections is below $x$, and using those 40 observations they are quite certain that that true value lies between $14.5$ and $17.5$.
The fact that what they're measuring (as far as I can see) is discrete (you can only have an integer number of connections at any one time) makes this somewhat confusing, but it seems that they are pretending that the observations take continuous values in order to make the analysis easier.