Transcript Ch 2 – The Normal Distribution YMS – 2.1

Ch 2 – The Normal Distribution
YMS – 2.1
Density Curves and
the Normal Distributions
Vocabulary
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Mathematical Model
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An idealized description of a distribution
Density Curve
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Is always on or above the horizontal axis
Has area = 1 underneath it
Can roughly locate the mean, median and
quartiles, but not standard deviation
Mean is “balance” point while median is
“equal areas” point.
Reminder: Exploring Data on a
Single Quantitative Variable
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Always plot your data
Identify socs
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Calculate a numerical summary to briefly
describe center and spread
Describe overall shape with a smooth curve
Label any outliers
Greek Notation
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Population mean is μ and population
standard deviation is σ
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These are for idealized distributions
(population vs. sample)
Classwork p83 #2.1 to 2.5
Next 2 classes – Fathom Activity and
Sketching WS
Activity: Beauty and the Geek
More Vocabulary
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Normal Curves
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Are symmetric, single-peaked and bell-shaped
They describe normal distributions
Inflection point
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Point where change of curvature takes place
Could use this to estimate standard deviation
3 Reasons for Using
Normal Distributions
1. They are good descriptions for some
distributions of real data.
2. They are good approximations to the results of
many kinds of chance outcomes.
3. Many statistical inference procedures based on
normal distributions work well for other
roughly symmetric distributions.
The 68-95-99.7 Rule
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In N(μ, σ), rule gives percent of data that
falls within 1, 2, and 3 standard
deviations, respectively.
AKA Empirical Rule
Classwork p89 #2.6-2.9
Homework p90 #2.12, 2.14, 2.18
and 2.2 Reading Blueprint
Sketch a bell curve for each of
the following:
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p(x
p(x
p(x
p(x
p(x
p(x
<
>
<
<
>
>
a ) = 0.5
b) = 0.5
c) = 0.8
d) = 0.2
e) = 0.05
f) = .95
YMS – 2.2
Standard Normal Calculations
Standards
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Standard Normal Distribution
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N(0, 1)
Standardized value of x (z-score)
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Data point minus mean divided by standard
deviation
Gives you the number of standard deviations
the data point is from the mean
Table A
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Left Column has ones.tenths digit
Top Row has 0.0hundreths digit
LEFT COLUMN + TOP ROW = Z-SCORE
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Area is always to the LEFT of the z-score
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TI-83 Plus
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Keystrokes
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2nd
DISTR
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1: normalpdf
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2: normalcdf(lower limit, upper limit, mean, st. dev.)
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Finds height of density curve at designated point
We won’t be using this
Gives area under the curve to left or right of a point
3:invNorm(area, mean, standard deviation)
*When you don’t enter a mean or standard deviation,
it assumes it is the Normal Distribution (0, 1)
In Class Exercises
p95 #2.19-2.20
Homework
p103 #2.21-2.25
Activity: Grading Curves WS
Normal Probability Plots (NPP)
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Is a plot of z-scores vs. data values
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Use the calculator!
If it’s a straight line, the data is normally
distributed.
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How else do we assess normality?
In Class Exercises
(Next 3 days)
Shape of Distributions WS
p108 #2.27
p113 #2.41-2.42, 2.46-2.47,
2.51-2.52, 2.54
AP Practice Packet