Download Lesson 7.4 Use Normal Distributions

Lesson 7.4 Use Normal
Distributions
Vocabulary
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• A normal distribution is
modeled by a bell-shaped
curve called a normal curve
that is symmetric about the
mean. The total area under
the related curve is 1.
• The percentage of the area
covered by each standard
deviation from the mean is
shown in the graph
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Standard Normal Distribution
• The standard normal distribution is the
normal distribution with mean 0 and standard
deviation 1.
• The formula below can be used to transform
x-values from a normal distribution with mean
x bar and standard deviation sigma into zvalues having a standard normal distribution.
z
xx

z-score
z
xx

• The z-value for a particular x-value is called
the z-score for the x-value and is the number
of standard deviations the x-value lies above or
below the mean .
Example 1
Example 2
• Oak Trees The heights
(in feet) of fully grown
white oak trees are
normally distributed
with a mean of 90 feet
and a standard
deviation of 3.5 feet.
• About what percent of
white oak trees have
heights between 86.5
feet and 93.5 feet?
Homework
• Page 266 1-18