I remember there is a result from the early 1980s, which states that the tail probability of a binomial distribution is always at least as large as the tail probability of the normal distribution (at least when $p \leq 1/4$ or something like this for the binomial distribution is assumed). However, I cannot rememeber the name of the theorem and the author, resp. Can someone help me?



Reference request: binomial tail is greater than Gaussian tail
You might be thinking of Eric V. Slud (1977), Distribution inequalities for the binomial law, <https://projecteuclid.org/download/pdf_1/euclid.aop/1176995801>, and you can find further related results proved or referenced in the thesis of Jona Schulz (2016), The optimal Berry–Esseen constant in the binomial case, <http://ubt.opus.hbz-nrw.de/volltexte/2016/1007/pdf/Dissertation_Schulz.pdf>


