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Contents Introduction: Normal distribution
· Introduction: Normal distribution
· The standard normal distribution
· More general normal distributions
· Solving problems by working backwards
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Introduction: Normal distribution
A sample of heights of 10,000 adult males gave rise to the
following histogram:
Notice that this histogram is symmetrical
and bell-shaped. This is the characteristic
shape of a normal distribution.
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Introduction: Normal distribution
If we were to draw a This is called the
smooth curve through the normal curve.
mid-points of the bars in
the histogram of these
heights, it would have the
following shape:
The normal distribution is an appropriate model for many
common continuous distributions, for example:
· The masses of new-born babies;
· The IQs of school students;
· The hand span of adult females;
· The heights of plants growing in a field;
etc.
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Introduction: Normal distribution
All normal curves are symmetrical and bell-shaped but the
exact shape is governed by 2 parameters ­ the mean, , and
the standard deviation, .
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Introduction: Normal distribution
If X has a normal distribution with mean , and variance 2,
we write
X ~ N [ , 2 ]
y
x
­ +
68% of the distribution lies within
1 standard deviation of the mean.
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