The distribution of the number of successes in $n$ independent trials is "bell-shaped". The expected number of successes, $\mu$ say, either determines the most probable number of successes uniquely or restricts it to the pair of integers nearest to $\mu$.
"On the Distribution of the Number of Successes in Independent Trials." Ann. Math. Statist. 35 (3) 1317 - 1321, September, 1964. https://doi.org/10.1214/aoms/1177703287