NSW Y12 Maths - Advanced Random Variables The Standard Normal Distribution

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The Standard Normal Distribution Theory

Calculating the \(z\) value. \[ z=\dfrac{x-\mu}{\sigma} \] where \(x\) is a random variable, \(\mu\) is the mean and \(\sigma\) is the standard deviation\\   \textbf{Example}\\ \(X\) is a random variable of a normal distribution with mean 8 and variance 4.  \((X-N(8,4))\)\\  Find the \(z\) value that would represent an \(x\) value of 10 .\\  \textbf{Solution}\\ $\begin{aligned} & z=\frac{x-\mu}{\sigma} \\ & z=\frac{10-8}{2} \\ & z=1 \end{aligned}$\\

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Videos

Videos relating to The Standard Normal Distribution.

  • The Standard Normal Distribution - Video - Finding Areas Under And What Is The Standard Normal Distribution Curve And Z Scores Explained

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  • The Standard Normal Distribution - Video - Using z scores to standardise and compare values

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