Continuity Correction
When approximating a discrete random variable (taking integer values k) with a continuous distribution, the discrete value k is represented as the interval (k - 0.5, k + 0.5). Thus, P(X = k) ≈ P(k - 0.5 < X_continuous < k + 0.5), and P(X ≤ k) ≈ P(X_continuous < k + 0.5).
Real World
Netflix models daily viewing hours (a discrete count) using a normal distribution to forecast server load — engineers apply continuity corrections to ensure probability estimates for exact viewing-hour values remain accurate.
Exam Focus
State your continuity correction explicitly: write P(X ≤ 5) ≈ P(Y < 5.5) — examiners award a mark for the correction itself.
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