Monotonicity of the binomial distribution function near the median

For the binomial random variable S with parameters n ∈ N and b/n its median is b if b ∈ {1, . . . , n}. In 2018, Dmitriev and Zhukovskii study the monotonicity by b of the function P(S b). In this paper this result is generalized to the random variable S with parameters n ∈ N and b/(n + c) for all c ∈ [0, 1], and the Dmitriev and Zhukovskii hypothesis is alsoconfirmed.