Section 2 · Lecture 09 · Sampling Distribution
When n is large, the Binomial distribution looks like a Normal curve with the same mean and variance, Y ≈ N(np, np(1 − p)), and the sample proportion follows p̂ ≈ N(p, p(1 − p)/n). Change n and p to see when the curve fits the bars, and how close the approximate answer is to the exact one.
Examples
Is n large enough? Both must be at least 5.
Calculate a probability
Work with
Question type
Continuity correction
About the continuity correction. Y takes only whole numbers, so each value k is a bar running from k − 0.5 to k + 0.5, while the Normal curve is continuous. The correction moves each boundary half a unit outwards (0.5/n on the p̂ scale) so that the Normal area covers every bar in the event. It is optional and usually brings the approximation closer to the exact answer. It is off by default, matching the lecture example.
Exact (Binomial)
Normal approximation
Difference, approximate − exact
The approximation, step by step