The density for the Normal distribution is shown as the black curve below: $$ f(y) = \frac{1}{\sqrt{2 \pi \sigma^2}} \exp\left[-\frac{1}{2} \frac{\left( y-\mu \right)^2}{\sigma^2} \right] $$

The CDF is the blue area under the curve. Its complement is shown in red.

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To calculate the CDF:

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To calculate the CDF's complement: