UNIT 3_05_LOCATING PERCENTILES UNDER THE NORMAL CURVE.pptx

STAT & PROB

1. LOCATING PERCENTILES UNDER THE NORMAL CURVE

2. PERCENTILE is a measure of relative standing. It is a descriptive measure of the relationship of a measurement to the rest of the data.

3. Example: In a test in Algebra, you got a score of 82 and you want to know how you fared in comparison with your classmates. If your teacher tells you that you score at the 90 th percentile, it means that 90% of the grades were lower than yours and 10% were higher.

4. … thus, when we are given the area and we wish to find the corresponding z-value, we locate the given area at the body of the table. If the exact area is not available, we take the nearest value . Then, we look up the corresponding z-value in the Table of Areas Under the Normal Curve or z-table.

5. Example 1: Having obtained a score of 85 in a recently concluded unit test in Science, John wanted to know how he fared in comparison with his classmates. His teacher told him that he scored at the 90 th percentile. What is the corresponding z-score of 90 th percentile? Step 1: Split 90% or 0.9000 into 0.5000+0.4000

6. Example 1: Having obtained a score of 85 in a recently concluded unit test in Science, John wanted to know how he fared in comparison with his classmates. His teacher told him that he scored at the 90 th percentile. What is the corresponding z-score of 90 th percentile? Step 2: Find the area of 0.4000 in the body of z-table. If it cannot be found in the table, get the area value nearest to it. The nearest value is 0.3997. Step 3: Identify the corresponding z-score of the area. The corresponding z-score is 1.28.

7. Example 1: Having obtained a score of 85 in a recently concluded unit test in Science, John wanted to know how he fared in comparison with his classmates. His teacher told him that he scored at the 90 th percentile. What is the corresponding z-score of 90 th percentile? Therefore, the z-score that corresponds to 90 th percentile on the normal curve is 1.28

8. Example 2: A score is in the 96 th percentile. Where is the score under the normal curve ? Step 1: Split 96% or 0.9600 into 0.5000+0.4600

9. Example 2: A score is in the 96 th percentile. Where is the score under the normal curve. Step 2: Find the area of 0.4600 in the body of z-table. If it cannot be found in the table, get the area value nearest to it. The nearest value is 0.4599. Step 3: Identify the corresponding z-score of the area. The corresponding z-score is 1.75

10. Example 2: A score is in the 96 th percentile. Where is the score under the normal curve. Therefore, the z-score that corresponds to 96 th percentile on the normal curve is 1.75

11. Example 3: Find the upper 10% of the normal curve. 10% is the same as 0.1000 0.5000 – 0.1000 = 0.4000 The nearest value is 0.3997 Step 1: Express the percentage as probability. Step 2: Using the upper side of the mean, find the remaining area. Step 3: Find the area of 0.4000 in the body of the z-table. If it cannot be found in the table, get the area value nearest to it.

12. Example 3: Find the upper 10% of the normal curve. The corresponding z-score is 1.28 Step 4: Identify the corresponding z-score of the found area Therefore, upper 10% is z = 1.28

13. Example 4: The results of a nationwide aptitude test in mathematics are normally distributed with an average of 80 and standard deviation of 15. What is the percentile rank of a score of 84?   Step 1: Convert the raw score of 84 to z-score form

14. Example 4: The results of a nationwide aptitude test in mathematics are normally distributed with an average of 80 and standard deviation of 15. What is the percentile rank of a score of 84? 0.1064 Step 2: Find the area corresponds to z = 0.27

15. Example 4: The results of a nationwide aptitude test in mathematics are normally distributed with an average of 80 and standard deviation of 15. What is the percentile rank of a score of 84? 0.5 + 0.1064 = 0.6064 0.6064 X 100 = 60.64% Step 3: Get the total area below z = 0.27 Step 4: Compute the percentile rank of the score 84. Therefore, the percentile rank of 84 is 60.64%.