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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

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)

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 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

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.

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

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?

Homework Assignment Worksheet

Ex. 13.21, 13.22

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