S1 Statistics Revision - Chapter 9 Notes

Chapter 9 - The normal distribution

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AS Statistics Revision
Statistics 1 ­ Chapter 9
The normal distribution
Key points to remember
The normal distribution = is symmetrical about its mean
has mode, median and mean all equal
ranges from to +
has a total area under the curve of unity
has notation N(, ²) where is the mean and ² is the
variance of the distribution
The standard normal distribution = the standard normal
variable
is denoted by Z where Z ~ N(0, 1²)
Any normal variable X, having a mean and variance ², can
be
transformed into a standard normal variable using:
(X ) ÷
Always remember that the denominator is .
A good clear diagram illustrating the area corresponding to
the
required probability should always be drawn. In the example
the
shaded area shows P(x(1) < X< x(2))

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