April 2026
Beginner
288 pages
5h 34m
English
Content preview from Probability Workbook For Dummies
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Chapter 10
Approximating a Binomial with a Normal Distribution
IN THIS CHAPTER
Understanding when the normal distribution can be used to approximate the binomial
Using the normal distribution to calculate probabilities for a binomial
Applying the continuity correction
The binomial distribution is popular because a lot of data comes from binomial (yes or no) scenarios. However, calculations with the binomial distribution get unwieldy when n reaches a certain point, and the table values run out, but you can do an approximation. The approximation you use turns out to be the normal approximation if the conditions for np and n(1 − p) hold. This works when n is sufficiently large. The normal approximation involves taking the binomial mean and standard deviation and putting them into the Z formula where 
and the mean and standard deviation (sd) come from the binomial. Recall from Chapter 8 that the mean of the binomial distribution is np, and the standard deviation is the square root of np(1 − p).
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