n=50

n=200

n=500

n = 0 (slider from 0 to 1000, step 1)
p = 0.35 (slider from 0 to 1, step 0.01)
np: n * p
σ: (n * p * (1 - p))^(0.5)
Y_{50} = Histogram(Sequence[k - 0.5, k, -50 * p, -50 * (p - 1) + 1, 1], Sequence[Binomial[50, k] * p^(k) * (1 - p)^(50 - k), k, 0, 50, 1])
Y_{200} = Histogram(Sequence[k - 0.5, k, -200 * p, -200 * (p - 1) + 1, 1], Sequence[Binomial[200, k] * p^(k) * (1 - p)^(200 - k), k, 0, 200, 1])
Y = Histogram(Sequence[k - 0.5, k, -n * p, -n * (p - 1) + 1, 1], Sequence[Binomial[n, k] * p^(k) * (1 - p)^(n - k), k, 0, n, 1])
σ_{50}: (50 * p * (1 - p))^(0.5)
σ_{200}: (200 * p * (1 - p))^(0.5)
Y_{500} = Histogram(Sequence[k - 0.5, k, -500 * p, -500 * (p - 1) + 1, 1], Sequence[Binomial[500, k] * p^(k) * (1 - p)^(500 - k), k, 0, 500, 1])
σ_{500}: (500 * p * (1 - p))^(0.5)