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Unformatted text preview: Notes 10 &ORMAL APPROXIMATIO& TO THE BI&OMIAL Recall : The parameters for the Binomial distribution are n and p . Binomial probability calculations become tedious when n is large. For a large sample size n and a suitable p, the Normal distribution can be used as a reasonable approximation for the Binomial model. This means that we can perform simpler Normal probability calculations instead to obtain close approximations for Binomial probabilities. The Normal approximation gets better as the sample size n increases; for a fixed value of n , it is more accurate for values of p close to 0.5 and less accurate for values of p close to 0 or 1. How do we decide when n is large enough for us to use the Normal approximation? When both np and nq are greater than or equal to 10, it is appropriate to use the &ormal approximation to the Binomial. It is therefore sufficient to check that the smaller of np and nq is greater than or equal to 10....
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