the number of pulls or spins) would need to be larger than 30, the magic number recommended by most applied statistics textbooks (Webster, 1998; Ott and Longnecker; 2010; Devore, 2012, to name a few) for the normal approximation
to yield accurate results.
This is the type of event for which the CLT can be used to justify a normal approximation
for this probability.
This result is a consequence of dependency graphs methods and a normal approximation
result of Chen and Shao  using the Stein method.
A hexagonal field of variation was calculated by means of normal approximation
including arithmetic means, standard deviations, and upper or lower confidence limits ([C.
In fact, an inspection of the new plot revealed that the LOGEPPG scores not only provided a better normal approximation
but also corrected the wedge-shaped pattern of the variances for the residual plot [Figure 3].
To rank these nine statements by the degree of gender difference (with 1 being the rank of the statement having the largest degree of gender difference) Z-values for the normal approximation
to the Mann-Whitney-Wilcoxon test were calculated.
for p using the normal approximation
to the binomial distribution (cf.
We provide normal approximation
error bounds for sums of the form [[summation].
The usual approach in such situations is to calculate the probability based upon the Poisson distribution or the normal approximation
to the binomial.