Bounds for median and 50 percetage point of binomial and negative binomial distribution

Inequalities for comparing the binomial distribution function/operating characteristic function with value 0.5 have been established long ago. It is a trivial task to infer from these inequalities bounds for the 50 percentage point of the binomial operating characteristic function. However, it is also possible to use these inequalities to establish good bounds for the median of the binomial distribution function. By a relation of binomial distribution function/operating characteristic function and negative binomial distribution function/operating characteristic function we can get bounds for the respective parameters of negative binomial distribution, too.