1 percentiles of normal distribution class 20. 2 class objective after this class, you will be able...
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Percentiles of Normal Distribution
Class 20
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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
•……………………………………
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Steps to use Z-score table to find the percentile of a raw score
1. Convert the raw score to standard score2. 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
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Quick Check (Show your steps)
• What is the percentile for the score 650?
• What is the percentile for the score 342?
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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 = 628Therefore, one has to get a score of 628 in order to be at the 90th percentile
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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?
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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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