Normal Approximation to the Binomial
Use the normal distribution to approximate binomial probabilities when the sample size is large enough.
Criteria for Use
The binomial random variable is approximately normal if the following condition is met:
If this condition is not met, the approximation may be inaccurate. Use exact binomial calculations or technology instead.
Parameters
When using the normal approximation, the binomial's mean and standard deviation become the normal's parameters:
Correction for Continuity
Since a continuous curve (normal) is used to approximate discrete values (binomial), you must add or subtract 0.5 from x. This is called the continuity correction.
To find
To find
Example: For , calculate using the normal distribution.
Try It Yourself
Normal Approximation Calculator
≥ 10
Parameters
For P(X ≤ 20), we use P(X < 20.5). Z = (20.5 - 20.00) / 3.46 = 0.1443
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