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Statistical Inference: A Short Course by Michael J. Panik

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6.3 Probability as An Area Under The Normal Curve

Suppose img is img If we are interested in finding img then we can do so by determining the area under the normal density curve from img (Fig. 6.5).

Figure 6.5 Probability as area under img.

img

(Note that when dealing with a continuous univariate probability density function, the notion of an “event” is simply an interval img on the X-axis.) While integral calculus techniques can be applied to find an area under the normal curve, we shall judiciously not attempt to do so. Instead, we shall read the area under the normal curve directly from a table. However, before we do so, let us note that there actually exists an infinite number of potential normal curves—one for each possible (allowable) value for . For instance, as increases in value from fixed, the normal ...

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