You can use this applet to investigate what the z-table values actually mean.<\/p>\n
In statistics, when we plot the distribution of a measurement (say, the heights of people) we very often produce the familiar bell-shaped curve. <\/p>\n
For example, the mean<\/strong> (average) height for males in the US is 175.5 cm and the standard deviation<\/strong> 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. <\/p>\n However, it is difficult to work out probabilities and proportions when the mean and standard deviations are different for each type of measurement. <\/p>\n The solution is to standardize<\/strong> 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<\/strong>. We can use a z-Table<\/a> 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.<\/p>\n The applet allows you to vary the mean and standard deviation, and upper and lower boundaries of the region of interest. <\/p>\n Here's a screen shot: <\/p>\n You can also see the calculations for your particular values.<\/p>\n 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.<\/p>\n The link again: Normal Probability Distribution Graph Interactive<\/a> <\/p>\n See the 4 Comments<\/a> below.<\/p>\n","protected":false},"excerpt":{"rendered":"The applet<\/h2>\n
![\"z-table](\"\/blog\/wp-content\/images\/2014\/02\/z-curve-screen-shot3.gif\")
<\/a><\/p>\nFor the geeks<\/h2>\n
![\"z-curve](\"\/blog\/wp-content\/images\/2014\/02\/z-curve_th2.gif\")
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