Under what conditions are you allowed to use the normal distribution to approximate the binomial distribution? Under what conditions might you want to use the normal distribution to approximate the binomial as opposed to using the binomial probability formula, a table of binomial probabilities, or a computer?
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Normal distribution can be used to approximate binomial distribution when the data on normal distribution is discrete
Conditions on how to use Normal distribution
U of computer , table or probability formulas are only to do exact calculations or if n is not very large, if X has the binomial distribution ie. X~ binomial (n,p) and
n is large, then X has approximately the Normal distribution with
mean µ=np and standard deviation . This approximation is reasonably good when np>10 and
Normal distribution can be used when the value of n is larger.
I will still continue to provide explanations.
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Jul 3rd, 2015
Normal distribution can be used under the following conditions
If n is large enough, then the skew of the distribution is not too great. In this case a reasonable approximation to B(n, p)
The following rule applies:
One rule is that both x=np and n(1 − p) must be
greater than 5. However, the specific number varies from source to
source, and depends on how good an approximation one wants; some sources
give 10 which gives virtually the same results as the following rule
for large n until n is very large .
Jul 3rd, 2015
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