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One of the difficulties students from basic courses often show in learning probability and statistics at the university is understanding how the continuous normal probability distribution approximates the discrete binomial probability distribution. In this paper a didactic proposal is presented consisting in two algorithms, very easy to use, developed with software R which is completely free. These algorithms aim to introduce students in basic concepts of normal approximation to the binomial distribution by means of graphical representations and tables. They allow an active participation of student in the learning process. [ABSTRACT FROM AUTHOR]

Several approximations to the binomial distribution were compared in 1956 by Raft [9], including the normal, arcsine, normal Gram-Charlier, Camp-Paulson, Poisson, and Poisson Gram-Charlier approximations. The closeness of these approximations is judged by the maximal error which can arise in evaluating any sum of consecutive binomial terms. Borges [3] investigated a general class of approximations (which includes some of the above) and showed that a certain beta-transformation of a binomially distributed variable is the unique member of this class which is approximately normal with error 0(l/n). In 1963, Bol'shev [2] gave two new Poisson-type approximations. In this paper, some of Raft's tables are extended and tables for the error of these newer approximations are added. As a consequence of the numerical results obtained, the Poisson Gram-Charlier approximation is recommended for small values of p while the Camp-Paulson and Borges' approximations should generally be preferred for large p. [ABSTRACT FROM AUTHOR]