Class 20
Percentiles of Normal Distribution
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Class Objective
After this class, you will be able to
- Use z-score table to find the percentile of
standard normal distribution
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Homework and Reading Check
• Assignment:
– Standard Score – Homework Worksheet
• Reading:
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From Histogram to Standard Normal
Distribution Curve
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Example: Percentiles for college
entrance exam
• Given: SAT score is normally distributed
: Mean = 500
: Standard deviation = 100
: Krystina’s raw score = 600
What is the z-score for Krystina?
What percentile of Krystina’s score would be ?
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Krystina is at the 84th percentile in the SAT exam.
What does that mean?
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If Alex gets 700, what percentile of the score is?
If Nicole gets 400, what percentile of the score is?
Challenge: If Henry gets 520, what percentile of the
score is ?
If Tiffany gets 480, what percentile of the score is ?
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Now, you have your “Standard Normal Distribution”
Table. How do you use it to find the percentile for
a raw score?
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When you have similar problems about finding a
percentile of a particular raw score, how do you
solve it? (Hints: List all the steps)
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Steps to use Z-score table to find the
percentile of a raw score
• Convert the raw score to standard score
•……………………………………
Steps to use Z-score table to find the percentile of a
raw score
1. Convert the raw score to standard score
2. If the standard score is a positive number, check the
“+ve” z-score table. Example 1.58
–
–
–
Look at the Z-VERTICAL Column (1.5)
Check the Z-HORIZONTAL Column (0.08)
Locate the corresponding percentile (.9429 / 94.29%)
3. If the standard score is a negative number, check the “ve” z-score table.
–
–
–
Look at the Z-vertical Column
Check the Z-horizontal column
Locate the corresponding percentile
Quick Check (Show your steps)
• What is the percentile for the score 650?
• What is the percentile for the score 342?
Challenge: If Jaime wants to be at the 90th
percentile, what score she needs to do get to do
that? List the steps if you know how to do it.
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Steps to find the raw score when percentile is
given
1. Locate the “closest” percentile in the z-score table (If the
given percentile is less than 50%, check the -ve z-score
table. If percentile is more than 50%, check the +ve z-socre
table) (example 90%, take the value of 0.9015)
2. Check the corresponding z-score. (1.28 for the value of
0.8997)
3. Convert the z-score back to raw score
= z-score x standard deviation + mean
= 1.28 x 100 + 500 = 628
Therefore, one has to get a score of 628 in order to be at
the 90th percentile
Quick Check (Show your steps)
• What raw score will make you stand at the 87
percentile?
• What raw score will make you stand at the 34
percentile?
The xth percentile of a distribution is a value such
that x percent of the observations lie below it and
the rest lie above?
What does that mean?
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Why the Z-table enable us to do calculations in
greater detail than does the 68-95-99.7 rule?
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Homework Assignment Worksheet
Ex. 13.21, 13.22
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