Resources for The Normal Distribution
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Questions
9
With Worked SolutionClick Here -
Video Tutorials
1
Click Here -
HSC Questions
6
With Worked SolutionClick Here
The Normal Distribution Theory
![Approximately \(68 \%\) of the distributions will lie within one standard deviation \((\sigma)\) of the mean \((\mu)\).\\ Approximately 95\% of the distributions will lie within two standard deviations of the mean.\\ Approximately \(99.7 \%\) of the distributions mill line within three standard deviations of the mean.\\ A continuous random variable that has a normal distribution with mean \(\mu\) and variance \(\sigma^2\) is written as \(X-N\left(\mu, \sigma^2\right)\)\\ \textbf{Example 1}\\ \(X-N(12,4)\) what is the range of values you would expect to find in: \\ (i) the middle \(68 \%\)\\ (ii) the middle \(95 \%\)\\ (iv) the middle \(99.7 \%\)\\ \textbf{Example 1 solution}\\ (i) \(\sigma^2=4 \rightarrow \sigma=2\). \[ \begin{aligned} \therefore 12-2<x & <12+2 \\ 10 & <x<14 \end{aligned} \] (ii) \(12-2 \times 2<x<12+2 \times 2\) \(8<x<16\)\\ (iii) \(12-3 \times 2<x<12+3 \times 2\) \[ 6<x<18 \]](/media/1cwednzl/26849.png)