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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
 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
 Finding Probabilities
 Using tables
Exam Practice
 Qu. 1
 Qu. 2
 Qu. 3
 Qu. 4
 Statistics Quiz