The Normal Distribution

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The Normal Distribution - PowerPoint PPT Presentation

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

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