TITLE: Why use 95% confidence interval?
QUESTION [9 upvotes]: May I ask why $95\%$ confidence is so commonly used? Does it have anything to do with $\frac{d}{d\alpha}e_n(\alpha)$, where $e_n(\alpha) = Z_{\alpha/2}\frac{S_n}{\sqrt n}$? (My professor asks me to evaluate this derivative at $\alpha = 0.05$, given $S_n = 4.7, n = 100$.)

REPLY [5 votes]: I don't think it is arbitrary because given a normal distribution 
68.27% of all values lie within 1 standard deviation
95.45% of all values lie within 2 standard deviations and
99.73% of all values lie within 3 standard deviations