Download M3A 11-3 Normal Distributions

Math III Accelerated
Chapter 11
Data Analysis
and Statistics
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Warm Up 11.3
 Simplify each expression. Round the answer
to the nearest hundredth.
93  97
1.
1 .5
20  18
2.
0 .8
3. 20.34   20.135
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11.3 Use Normal Distributions

Objective:
 Study normal distributions.
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Vocabulary
 Normal Distribution
A probability distribution modeled by a bell
shaped curve that is symmetric about the
mean.
 Normal Curve
The bell shaped curve that models a normal
distribution.
 Standard Normal Distribution
The normal distribution with mean = 0 and
standard deviation = 1.
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Properties of the Normal Distribution
x
 Bell-shaped curve with the highest point over the mean.
 The curve is symmetric about the mean.
 The curve approaches the horizontal axis but never
touches or crosses it.
 Total area under the curve = 1.
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Area Under A Normal Curve
 Approximately 68% of the data values lie
within one standard deviation of the mean.
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Area Under A Normal Curve
 Approximately 95% of the data values lie
within two standard deviations of the mean.
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Area Under A Normal Curve
 Almost all (approximately 99.7%) of the
data values will be within three standard
deviations of the mean.
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Example 1
 A normal distribution has mean x and
standard deviation σ. For a randomly
selected x-value from the distribution,
find the probability that the x-value lies
between x and x + 3σ.
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Checkpoint 1
 A normal distribution has mean x and
standard deviation σ. For a randomly
selected x-value from the distribution,
find the probability that the x-value lies
between x and x – σ.
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Example 2
 The math scores of the 2004 SAT exam are
normally distributed with a mean of 518
and a standard deviation of 114.
a. About what percent of the test-takers have
scores between 518 and 746?
b. About what percent of the test-takers have
scores less than 404?
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Checkpoint 2
 The math scores of the 2004 SAT exam are
normally distributed with a mean of 518
and a standard deviation of 114. About
what percent of the test-takers have scores
between 404 and 632?
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Example 3
 The blood cholesterol readings for a group
of women are normally distributed with a
mean of 172 mg/dl and a standard
deviation of 14 mg/dl.
a. About what percent of the women have
readings between 158 and 186?
b. Readings higher than 200 are considered
undesirable. About what percent of the
readings are undesirable?
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Homework 11.3
 Practice 11.3
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