Grade 11-Normal Distribution DAvila.pptx

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1. 11 Statistics and Probability

2. OPENING PRAYER Father God, Come be with us today. Fill our hearts with joy. Fill our minds with learning. Fill our classrooms with peace. Fill our lessons with fun. Fill our friendships with kindness. Fill our school with love. Amen.

3. Normal Distribution

4. “ARE YOU FAMILIAR WITH ME?” Direction: Determine the name of the following symbol. PRE- ACTIVITY

5. Familiarize me! Standard Deviation x bar for mean Sigma for standard deviation Mu for mean

6. objectives Illustrates a normal random variable and its characteristics. Draw a normal curve State the Empirical Rule

7. Let’s recall!

8. lesson 1 : Normal distribution What is a Normal Distribution?

9. lesson 1 : Normal distribution

10. lesson 1 : normal distribution

11. lesson 1 : normal distribution It is also called as BELL Shape or Normal Curve

12. lesson 1 : normal distribution PROPERTIES OF A NORMAL DISTRIBUTION The   mean, mode and median  are all equal. The curve is symmetric at the center (i.e. around the mean, μ ). Exactly half of the values are to the left of center and exactly half the values are to the right. The total area under the curve is 1.

13. The following variables are close to normally distributed variables: Height of a population Blood pressure of adult human Position of a particle that experiences diffusion Measurement errors Residuals in regression Shoe size of a population Amount of time it takes for employees to reach home A large number of educational measures

14. lesson 1 : normal distribution The Normal Distribution has two parameters . The mean that denoted as  μ The standard deviation that denoted as  σ

15. Mu or population mean

16. Mu or population mean

17. Sigma or population standard deviation

18. Sigma or population standard deviation The larger the standard deviation, the more spread out the distribution will be. As the spread increases, the curve gets much flatter. The smaller the standard deviation, the less spread out the distribution will be. And the spread decreases the curve gets taller.

19. lesson 1.1 : empirical rule 68-95-99.7 rule

20. lesson 1.1 : empirical rule 68-95-99.7 rule Within one standard deviation away from the mean it contains of total area of 68%. Within two standard deviation away from the mean it contains of total area of 95%. Within three standard deviation away from the mean it contains of total area of 99.7%.

21. lesson 1.1 : empirical rule 68-95-99.7 rule Example 1: The normal distribution below has a standard deviation of 10. Approximately what area is contained between 70 and 90?

22. lesson 1.1 : empirical rule 68-95-99.7 rule Example 1: The normal distribution below has a standard deviation of 10. Approximately what area is contained between 70 and 90?

23. lesson 1.1 : empirical rule 68-95-99.7 rule Example 1: The normal distribution below has a standard deviation of 10. Approximately what area is contained between 70 and 90?

24. lesson 1.1 : empirical rule 68-95-99.7 rule Example 2: For the normal distribution below approximately what area is contained between -2 and 1?

25. lesson 1.1 : empirical rule 68-95-99.7 rule Example 2: For the normal distribution below approximately what area is contained between -2 and 1?

26. lesson 1.1 : empirical rule 68-95-99.7 rule Example 2: For the normal distribution below approximately what area is contained between -2 and 1?

27. lesson 1.1 : empirical rule 68-95-99.7 rule Example 2: For the normal distribution below approximately what area is contained between -2 and 1?

28. lesson 1.1 : empirical rule 68-95-99.7 rule Example 2: For the normal distribution below approximately what area is contained between -2 and 1?

29. lesson 1.1 : empirical rule 68-95-99.7 rule Example 2: For the normal distribution below approximately what area is contained between -2 and 1?

30. ACTIVITY TRY THIS! Use the Empirical Rule to complete the table. Write on the perspective column the range or interval of the scores based on the given parameters. 107 - 163 547 - 587 198 - 228 81.5 – 92.5 756 - 814 79 - 191 76 - 98 183 - 243 527 - 607 727 - 843 51 - 219 70.5 – 103.5 168 - 258 507 - 627 698 - 872

31. Assignment

32. Direction : Read and understand the given problem carefully. Apply the empirical rule and illustrate your answer through a diagram. 1. IQ scores of the ALS students in the Division of Naga City are normally distributed with a mean of 110 and a standard deviation of 10. a. What percent of the distribution falls within the IQ scores of 100 to 130? b. What percent of the distribution falls within the IQ scores of 90 to 140?

33. closing PRAYER We thank you Lord, for the knowledge we learned today. Please help us to become your worthy children to glorify you.

34. REFERRENCES Normal Distribution by Simple Pro Learning Elementary Statistics – Eight Edition by Allan G. Bluman Statistics Module - NCSHS