# normal distribution

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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?

Jul 3rd, 2015

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 n(1-p)>10.  Normal distribution can be used when  the value of n is larger.

I will still continue to provide explanations.

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(np)

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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Jul 3rd, 2015
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Jul 3rd, 2015
Nov 18th, 2017
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