I try to approximate inverse CDF of BinomialDistribution with inverse CDF of NormalDistribution. Works pretty well, but there is a noticeable bias, that may be a sign of some imprecision or bias in either BinomialDistribution.inverseCumulativeProbability(), or NormalDistribution.inverseCumulativeProbability(), or both.
See https://stats.stackexchange.com/questions/392281/approximation-of-inverse-cdf-of-binomial-distribution-with-inverse-cdf-of-normal .