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Illuminating Statistical Analysis Using Scenarios and Simulations by Jeffrey E. Kottemann

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15The z-Distribution

If we use a continuous line to connect the tops of each bar of the general-purpose standardized normal distribution histogram from the previous chapter, we get a shape that looks like Figure 15.1.

img

Figure 15.1

If we repeat the simulation many more times and use narrower bars, we get the smoother curve as shown in Figure 15.2.

img

Figure 15.2

If we could repeat the simulation an infinite number of times and could make the histogram bars infinitely narrow, we would get a general-purpose normal distribution curve that is perfectly smooth and continuous. It is called the img-distribution and is shown in Figure 15.3. It is a very important probability distribution.

A graphical representation for z-distribution, where frequency is plotted on the y-axis on a scale of 0–0.5 and #SEs (z) on the x-axis on a scale of -4.5–4.5.

Figure 15.3

The img-distribution is a probability distribution that is normal, standardized, and continuous. Since it is a probability distribution, the entire area under the curve is 1. And, since the bars are infinitely narrow, probabilities for specific values—such the probability of #SEs exactly equaling ...

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