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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) – 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 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- 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 Exam Practice Qu. 1 Qu. 2 Qu. 3 Qu. 4 Statistics Quiz