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Math 2201
Section 5.4
5.4 The Normal Distribution
In many situations, if a controlled experiment is repeated and the data is collected to create a histogram,
the histogram becomes more and more bell-shaped as the number of data in the distribution increases.
Such repeated measurements will produce bell-shaped distributions which exhibit the characteristics of
a normal curve.
o The ______________________________ is shaped like a ______________, peaking at the
middle and tapering off at the extremes. (Also called the ________________________)
o The graph is symmetrical. The mean, median and mode are equal (or close) and fall in the
vertical line of symmetry.
o About ______________ of the data fall within one standard deviation of the mean.
o About ______________ of the data fall within two standard deviations of the mean.
o About ______________ of the data fall within three standard deviations of the mean.
o Generally measurements of living things such as mass, height & lifespan have a normal
distribution.
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Math 2201
Section 5.4
Low Standard Deviation vs High Standard Deviation
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Math 2201
Section 5.4
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Math 2201
Section 5.4
Example 2
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Math 2201
Section 5.4
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Math 2201
Example 5:
Section 5.4
The assessed value of housing in Bay Roberts is normally distributed.
There are 1200 houses with a mean assessed value of $180 000. The
standard deviation is $10 000. Draw a normal curve to represent the
data and use it to answer the following questions:
a) What percentage of houses have an assessed value between $170 000 and $200 000?
b) What percentage of houses have an assessed value less than $200 000?
c) About how many houses have an assessed valued between $170 000 and $200 000?
d) About how many houses have an assessed value greater than $190 000?
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