high School⏱ 4 min

Binomial Distribution

Number of successes in n trials

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0124.4%311.7%420.5%524.6%620.5%711.7%84.4%910μ=5.0
n = 10
p = 0.50
P(X=k)=\inomnkpk(1−p)n−kP(X=k) = \inom{n}{k}p^k(1-p)^{n-k}
μ=np=5.00,σ2=np(1−p)=2.50\mu = np = 5.00, \quad \sigma^2 = np(1-p) = 2.50

Binomial distribution: n trials, each with probability p. As n grows with p=0.5, the shape approaches the normal distribution (CLT).