This approximation, known as de Moivre–Laplace theorem, is a huge time-saver when undertaking calculations by hand (exact calculations with large are very onerous); historically, it was the first use of the normal distribution, introduced in Abraham de Moivre's book The Doctrine of Chances in 1738. Nowadays, it can be seen as a consequence of the central limit theorem since is a sum of independent, identically distributed Bernoulli variables with parameter . This fact is the basis of a hypothesis test, a "proportion z-test", for the value of using , the sample proportion and estimator of , in a common test statistic.NIST/SEMATECH, "7.2.4. Does the proportion of defectives meet requirements?" e-Handbook of Statistical Methods.
This approximation known as de Moivre–Laplace theorem is a huge time-saver when undertaking calculations by hand (exact calculations with large are very onerous); historically it was the first use of the normal distribution introduced in Abraham de Moivre's book The Doctrine of Chances in 1738 Nowadays it can be seen as a consequence of the central limit theorem since is a sum of independent identically distributed Bernoulli variables with parameter  This fact is the basis of a hypothesis test a "proportion z-test" for the value of using  the sample proportion and estimator of  in a common test statisticNIST/SEMATECH "724 Does the proportion of defectives meet requirements" e-Handbook of Statistical Methods