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Unimodal and symmetric; the “bell-shaped curve”
It is a theoretical model and not meant to fit data exactly. Remember this is the real world!
It is based on
of a population, not the summary statistics we calculated.
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The normal model is based on mean and standard deviation
750 1000 1250 1500 1750 2000 2250

Example: Two tests that are normally distributed.
Both with a mean of 84 but the 1 st had a standard deviation of 3 and the 2 nd had a standard deviation of 5.
The mean defines the center and standard deviation defines the spread.
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About 68% of the values fall within 1 st. dev. of the mean
About 95% of the values fall within 2 st. dev. of the mean
About 99.7% of the values fall within 3 st. dev. of the mean.
68%
95%
99.7%
750 1000 1250 1500 1750 2000 2250
About 68% of SAT scores lie between 1250 and 1750
About 95% of SAT scores lie between 1000 and 2000
About 99.7% of SAT scores lie between 750 and 2250
57 59.5
62 64.5
67 69.5
72
About 68% of heights lie between 62” and 67”
About 95% of heights lie between 59.5” and 69.5”
About 99.7% of heights lie between 57” and 72”

Hit
Select 2:normalcdf(
Needs 4 Numbers:
1.
Lower Bound
2.
3.
4.
Upper Bound
Mean
St. Dev.
Examples: SAT Scores N(1500,250)
What percent of SAT scores are less than 1800?
What percent of SAT scores are less than 1250?
What percent of SAT Scores are below 1620?
Lower Bound is -10^99
P(x < #) normalcdf(-10^99,#,mean,st.dev)
Example: What percent of SAT Scores are less than 1400?
N(1500, 250)
Use the calculator: normalcdf(-10^991400,1500,250)
Notation: P(x < 1400) = 34.46%
Upper Bound is 10^99
P(x > #) normalcdf(#,10^99,mean,st.dev)
Example: What percent of SAT Scores are greater than 1600?
N(1500, 250)
Use the calculator: normalcdf(1600,10^99,1500,250)
Notation: P(x > 1600) = 34.46%

Example: SAT Scores N(1500,250)
What percent of SAT scores are greater than 1750?
What percent of SAT scores are greater than 2000?
What percent of SAT Scores are more than 1000?
P(#1 < x < #2) normalcdf(#1,#2,mean,st.dev)
Example: What percent of SAT Scores are between 1400 and 1600?
N(1500, 250)
Use the calculator: normalcdf(1400,1600,1500,250)
Notation: P(1400 < x < 1600) = 31.08%
Example: SAT Scores N(1500,250)
What percent of SAT scores are between 1250 and1750?
What percent of SAT scores are between 1500 and 1750?
What percent of SAT Scores are between 1500 and 2000?

What percent of the students scored between
61 and 79?
P(61 < x < 79) = 68.27%
What percent of students scored above 79?
P(x > 79) = 15.87%
What percent of students scored below 59?
P(x < 59) = 11.08%
What percent of students scored below 75?
P(x < 75) = 71.07%
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What percent of students score between 75 and
100?
P(75 < x < 100) = 28.88%
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What percent of students scored between 60 and
80?
P(60 < x < 80) = 73.35%
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What percent of students scored between 80 and
90?
P(80 < x < 90) = 12.01%
What percent of students scored higher than 90?
P(x > 90) = 1.31%
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We standardize in the same way:
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Called the
-score.
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The model N(0,1) is the standard Normal model