Normal Approximation Example

Probability · Axiom Academy

EXAMPLE Normal Approximation to Binomial Comparing exact binomial with normal approximation and continuity correction Excellent work! You've completed this example. Here's what we learned: Rule of thumb: Normal approximation to binomial is good when np ≥ 10 and n(1-p) ≥ 10. Here, 100(0.3) = 30 and 100(0.7) = 70, so both conditions are satisfied. Continuity correction matters: The approximation with correction (0.1292) is much closer to the exact value (0.1314) than without correction (0.1056). Why correct from 25 to 25.5: The discrete value X ≤ 25 corresponds to the continuous interval (-∞, 25.5] when approximating with a continuous distribution. Practical advantage: Normal approximation avoids computing 26 binomial probabilities individually, making calculations much faster for large n. Continuity correction bridges discrete and continuous distributions, significantly improving approximation accuracy!

This is the written version of the interactive lesson above. See the full Probability course.