# New z-Table interactive graph

By Murray Bourne, 03 Feb 2014

I recently added a new interactive item to the Counting & Probability chapter:

Normal Probability Distribution Graph Interactive

You can use this applet to investigate what the z-table values actually mean.

In statistics, when we plot the distribution of a measurement (say, the heights of people) we very often produce the familiar bell-shaped curve.

For example, the **mean** (average) height for males in the US is 175.5 cm and the **standard deviation** is 7.4 cm. When we plot the heights of US males, we get a bell-shaped (also known as Gaussian) curve. We know that around 68% of US males have heights between 168.1 cm (one standard deviation below the mean) and 182.9 cm (one standard deviation above the mean.

However, it is difficult to work out probabilities and proportions when the mean and standard deviations are different for each type of measurement.

The solution is to **standardize** the measurements which means we translate the mean to 0 and the standard deviation to 1. When we graph this resulting distribution, we get the **standard normal curve**. We can use a z-Table to find probabilities of certain events occurring. The z-Table tells us the area under the standard normal curve for particular values of interest, thus telling us the probability of an event.

## The applet

The applet allows you to vary the mean and standard deviation, and upper and lower boundaries of the region of interest.

Here's a screen shot:

You can also see the calculations for your particular values.

## For the geeks

This math applet uses JSXGraph, jQuery and MathJax. It works on tablets, albeit a bit slow. One of the challenges when developing this was to make it as efficient as possible.

The link again: Normal Probability Distribution Graph Interactive

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