Section 5.1
Summer 2013 - Math 1040
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Roadmap
Normal Distributions
Normal distributions - µ, σ
Normal curves & pdfs.
The standard normal distribution.
Areas under the standard normal curve.
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A Normal Distribution
A normal distribution is a continuous distribution with a symmetric,
bell-shaped curve. The mean, median, and mode occur at the same place.
One standard deviation from the mean is where the curve inflects.
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Normal Curves
Curves can have the same mean, but different standard deviations.
µ = 3.5, σ1 = 1.5, σ2 = 0.7
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Normal Curves
What will curves with different means, but the same standard deviations
look like?
µ1 = 3.5, µ2 = 1.5, σ = 1.5
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Normal Distributions
Each normal distribution has its own mean and standard deviation. The
normal distribution with mean 0 and standard deviation 1 is called the
standard normal distribution.
z-scores transform any normal random variable x into the standard normal
distribution.
x −µ
σ
Round this value to the nearest hundredth.
z=
Standard normal tables match a z-score with a cumulative area value.
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Areas to the left of z
Use the table to find the area for the z-score.
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Areas to the right of z
Find the area. Then subtract it from 1.
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Areas in between two z-scores
Find both areas. Subtract the smaller from the larger.
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Assignments
Assignment:
1
Read pages 236 - 243.
2
Page 244: 1 - 59 odd.
Vocabulary: normal distributions, normal curves, probability density
functions, z-scores, standard normal distribution
Understand: How to draw a normal distribution curve. Compute z-scores.
Find areas under the standard normal curve using a table.
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