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The Normal Distribution

The Normal Distribution. AS Mathematics Statistics 1 Module. Introduction :. The Normal Distribution X~N( , 2 ) where  is the population mean and  2 is the population variance The distribution is symmetrical about the mean,  and all the averages (mean, mode and median coincide)

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The Normal Distribution

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  1. The Normal Distribution AS Mathematics Statistics 1 Module

  2. Introduction : • The Normal Distribution • X~N(,2) where  is the population mean and 2 is the population variance • The distribution is symmetrical about the mean,  and all the averages (mean, mode and median coincide) • The distribution can be plotted as a frequency polygon where the total area under the curve equal 1 • The curve will extend to - to the left and +  to the right • The curve

  3. Comparing Theory and Experimental Observations • In reality, like all probability work, the results you obtain using probability theory will not coincide exactly with actual observations. This is true for Normal Distribution as well. • However, if a large enough sample is taken it can be seen that the Normal Distribution model will closely follow observed results. • Experiment and Theory • Calculating Normal Distribution probabilities involves standardising an experiment using Z~N(0,1) where z =x- 

  4. Calculating Probabilities • Normal distribution probabilities are calculated by using a complicated formulae, luckily you do not need to know this formulae as all the results have been calculated and put into Normal Distribution tables for the Standardised Distribution of Z~N(0,1) • Finding Probabilities • Using tables

  5. Exam Practice • Qu. 1 • Qu. 2 • Qu. 3 • Qu. 4 • Statistics Quiz

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