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)
σ_{50}: (50 * p * (1 - p))^(0.5)
probasX = Sequence(Binomial[n, k] * p^(k) * (1 - p)^(n - k), k, 0, n)
probasX_{50} = Sequence(Binomial[50, k] * p^(k) * (1 - p)^(50 - k), k, 0, 50)
abscissesT_{50} = Sequence((k - 50 * p - 0.5) / σ_{50}, k, 0, 51, 1)
σ_{200}: (200 * p * (1 - p))^(0.5)
σ_{500}: (500 * p * (1 - p))^(0.5)
probasX_{200} = Sequence(Binomial[200, k] * p^(k) * (1 - p)^(200 - k), k, 0, 200)
probasX_{500} = Sequence(Binomial[500, k] * p^(k) * (1 - p)^(500 - k), k, 0, 500)
abscissesT = Sequence((k - n * p - 0.5) / σ, k, 0, n + 1, 1)
abscissesT_{200} = Sequence((k - 200 * p - 0.5) / σ_{200}, k, 0, 201, 1)
abscissesT_{500} = Sequence((k - 500 * p - 0.5) / σ_{500}, k, 0, 501, 1)
Z_{50} = Histogram(abscissesT_{50}, probasX_{50} * σ_{50})
Z_{200} = Histogram(abscissesT_{200}, probasX_{200} * σ_{200})
Z_{500} = Histogram(abscissesT_{500}, probasX_{500} * σ_{500})
Z = Histogram(abscissesT, probasX * σ)