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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)

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the normal distribution

The Normal Distribution

AS Mathematics

Statistics 1 Module

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