One reason the Normal approximation may fail to give accurate
estimates of binomial probabilities is that the binomial
distributions are discrete and the Normal distributions are
continuous. That is, counts take only whole number values, but
Normal variables can take any value. We can improve the Normal
approximation by treating each whole number count as if it occupied
the interval from 0.50.5 below the number to 0.50.5 above the
number. For example, approximate a binomial probability
?(?≥10)P(X≥10) by finding the...