The Normal Distribution AS Mathematics Statistics 1 Module

Introduction : 4 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 4 The curve The curve

Comparing Theory and Experimental Observations 4 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. 4 However, if a large enough sample is taken it can be seen that the Normal Distribution model will closely follow observed results. 4 Experiment and Theory Experiment and Theory 4 Calculating Normal Distribution probabilities involves standardising an experiment using Z~N(0,1) where z = x-  

Calculating Probabilities 4 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) 4 Finding Probabilities Finding Probabilities 4 Using tables Using tables

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