統計學～樣本比率值超過50%的機率?

X～bin(1oo,o.6)
P[X/1oo > o.5] = P[X > 5o]
     = Σ_{k > 50} C(100,k)(0.6)^k(0.4)^(100-k)

用常態近似:
μ = np = 60
σ^2 = np(1-p) = 24, σ = √24 = 4.898979

P[X > 50] = 1 - P[X ≦ 50]
    = 1 - P[Z ≦ (50.5-60)/4.898979]
    = 1 - P[Z ≦ -1.939]
    = 1 - P[Z ≧ 1.939]     (∵ 對稱性)
    = P[Z ≦ 1.939]
    = 0.97375    (查表)