Normal Approximation to Binomial
For large n, a binomial distribution B(n, p) can be approximated by a normal distribution N(np, np(1-p)), provided np ≥ 5 and n(1-p) ≥ 5.
Real World
An election pollster surveying 500 voters where historically 45% support a party uses N(225, 123.75) to estimate the probability of getting fewer than 210 supporters, rather than summing hundreds of binomial terms.
Exam Focus
Always apply continuity correction: P(X ≤ 209) becomes P(X < 209.5) in the normal approximation — examiners penalise its omission.
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