The "S"
Curve
Recall that the cumulative probability accumulates from 0 to
1 regardless of the actual distribution being summed or integrated. We can
easily equate the accumulating value as accumulating from 0 to 100%. For
example, if we accumulate all the values in a Normal distribution between
±1σ of the mean, we will find 68.3% of the total
value of the cumulative total. We can say with 68.3% "confidence" that an
outcome from a Normal distribution will fall in the range of ±1σ of the mean; the corollary is that with 31.7% confidence,
an outcome will lie outside this range, either more pessimistic or more
optimistic.
Integrating the Normal curve produces an "S" curve. In general,
integrating the BETA and Triangular curves will also produce a curve of roughly
an "S" shape. [23] Figure 2-7 shows the "S" curve.
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