Last year I made a couple of models on Desmos to demonstrate aspects of the normal distribution to my statistics students.

**1. Standardising**

In this first one, you can set a normal distribution with any mean and standard deviation and then show what happens when you subtract *μ* and divide by *σ* to standardise the distribution (to do this, simply move the sliders). It’s great because students can now visualise the procedure they are carrying out.

**2. Area Under the Normal Distribution Curve**

In this one you move the sliders for ‘a’ and ‘b’ to demonstrate P(Z<a) or P(Z>b). You can hide/reveal shading for the area in question, the remaining area and any equivalent area reflected in the y-axis as and where appropriate. To hide/reveal areas, click on the circles on rows 7, 9, 10, 15, 17 or 19.

Have a play and use them how you see fit.

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[…] But you don’t need to know the CDF to represent it in Desmos, you just need to use inequalities to shade the region between the x-axis and the curve, with a slider for the variable value of x. The syntax is a little unusual, but take a look and you’ll see how it’s done. The same principle was used in my model for normal distribution. […]

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