Quarter 3 Statistics and Probability PPT

Statistics and Probability

1. Based on the graph, identify and shade the regions under the curve. 1. z = 0 to z = 1 2. z = -1 to z = 2 3. z = -2 to z = 0

2.       Notations - A system of symbols used to represent special things.

3. Learning Competency: Identifies regions under the normal curve corresponding to different standard normal values (M11/12SP-IIIc-3) Unpacked of MELCs Identify the probability notations under the normal curve

4. Tabulate and identify the words that are synonymous to “greater than” and “less than” at least at most no more than to the right of more than to the left of not greater than above below Group Activity

5. Answers: greater than (>) less than (<) at least more than to the right of above at most no more than not greater than to the left of below

6. a b   - that a is less than b a b   - that a is greater than b a b   - that c is between a and b

7. P(z b)   - the probability that the z-score is less than b P(z )   - the probability that the z-score is greater than a P(a b)   - the probability that the z-score is between a and b Learning the Probability Notations Under the Normal Curve

8. Statement Notation 1. Find the area below z = 2 Ex. Find the proportion of area to the right of z = 0 P(z > 0) 2. Find the area between z = -1.30 and z = 3 P(z < 2) P(-1.30< z < 3) Activity 7 Find the area if z is no more than 1 P(z < 1) Identify the appropriate notation of the area under the curve and graph the given statement.

9. Statement Notation Quiz 7 1. Find the proportion of the area above z = -1 2. Find the area to the left of z = -1.5 3. Find the area between z = -2.5 and z = 2.95 P(z > -1) P(z < -1.5) P(-2.5< z < 2.95) Identify the appropriate notation of the area under the curve and graph the given statement.

10. Assignment Study on how to compute the Z-score

11. Where can we find the of central tendencies in the normal curve?

12. Where can we find the of central tendencies in the normal curve?

13. What are the synonyms of greater than and less than ? greater than (>) less than (<) at least more than to the right of above at most no more than not greater than to the left of below

14. Statement Notation 1. Find the proportion of the area above z = -1 2. Find the area to the left of z = -1.5 3. Find the area between z = -2 and z = -1.5 P(z > -1) P(z < -1.5) P(-2< z < -1.5)

15. Learning Competencies: Identifies regions under the normal curve corresponding to different standard normal values (M11/12SP-IIIc-3) Unpacked of MELCs Find the regions under the normal curve that corresponds to different standard normal values

16. Modified Steps in Determining Areas Under the Normal Curve 1. Draw a normal curve 2. Locate the z – value 3. Draw a line through the z – value 4. Shade the required region 5. In the z – table, find the area that corresponds to the z – value 6. Examine the graph and use probability notation to form an equation showing an appropriate operation to get the required area 7. Make a statement indicating the required area

17. Example Case No. 1 1. Find the proportion of the area above z = -1 Steps Solution 1. Draw a normal curve 2. Locate the z – value 3. Draw a line through the z – value 4. Shade the required region 5. In the z – table, find the area that corresponds to the z – value z = -1 corresponds to an area of 0.3413

18. Steps Solution 6. Examine the graph and use probability notation to form an equation showing an appropriate operation to get the required area The graph suggests addition The required area is equal to = 0.5+ 0.3413 = 0.8413 P(z>-1) 7. Make a statement indicating the required area The proportion of the area above z = -1 is 0.8413 Find the proportion of the area above z = -1

19. Case No. 2 2. Find the area to the left of z = -1.5 Steps Solution 1. Draw a normal curve 2. Locate the z – value 3. Draw a line through the z – value 4. Shade the required region 5. In the z – table, find the area that corresponds to the z – value z = -1.5 corresponds to an area of 0.4332

20. Steps Solution 6. Examine the graph and use probability notation to form an equation showing an appropriate operation to get the required area The graph suggests subtraction The required area is equal to = 0.5 – 0.4332 = 0.0668 P(z<-1.5) 7. Make a statement indicating the required area The proportion of the area to the left of z = -1.5 is 0.0668 Find the area to the left of z = -1.5

21. Find the area of the following z – values: 1. the area greater than z = 1 2. the area below z = 1.5 Activity 8:

22. Answers: 1. Find the area greater than z = 1 Steps Solution 1. Draw a normal curve 2. Locate the z – value 3. Draw a line through the z – value 4. Shade the required region 5. In the z – table, find the area that corresponds to the z – value z = 1 corresponds to an area of 0.3413

23. Steps Solution 6. Examine the graph and use probability notation to form an equation showing an appropriate operation to get the required area The graph suggests subtraction The required area is equal to = 0.5 - 0.3413 = 0.1587 P(z>1) 7. Make a statement indicating the required area The proportion of the area greater than z = 1 is 0.1587

24. 2. Find the area below of z = 1.5 Steps Solution 1. Draw a normal curve 2. Locate the z – value 3. Draw a line through the z – value 4. Shade the required region 5. In the z – table, find the area that corresponds to the z – value z = 1.5 corresponds to an area of 0.4332

25. Steps Solution 6. Examine the graph and use probability notation to form an equation showing an appropriate operation to get the required area The graph suggests addition The required area is equal to = 0.5 + 0.4332 = 0.9332 P(z<1.5) 7. Make a statement indicating the required area The proportion of the area below z = 1.5 is 0.9332

26. Find the area of the following z – values: 1. below z = - 0.58 2. to the left of z = 2.78 Quiz 8:

27. Answers: 1. Find the area below z = - 0.58 Steps Solution S1 S2 S3 S4 z = -0.58 corresponds to an area of 0.2190 S5

28. Steps Solution S6 S7 The graph suggests subtraction The required area is equal to = 0.5 - 0.2190 = 0.2810 P(z<-0.58) The proportion of the area below z = - 0.58 is 0.2810

29. 2. Find the area to the left of z = 2.78 Steps Solution S1 S2 S3 S4 z = 2.78 corresponds to an area of 0.4973 S5

30. Steps Solution S6 S7 The graph suggests addition The required area is equal to = 0.5 + 0.4973 = 0.9973 P(z<2.78) The proportion of the area to the left of z = 2.78 is 0.9973

31. Assignment Study on how to compute and shade the “in between area” when the z-score is given (Case no. 3 and 4).

32. What are the synonyms of greater than and less than ? greater than (>) at least more than to the right of above less than (<) at most no more than not greater than to the left of below

33. Learning Competencies: Identifies regions under the normal curve corresponding to different standard normal values (M11/12SP-IIIc-3) Unpacked of MELCs Find the regions under the normal curve that corresponds to different standard normal values

34. Case No. 3 1. Find the area between z = -2 and z = -1.5 Steps Solution S1 S2 S3 S4 S5 z = -2 corresponds to an area of 0.4772 z = -1.5 corresponds to an area of 0.4332

35. Steps Solution S6 The graph suggests subtraction The required area is equal to = 0.4772 – 0.4332 = 0.0440 P(-2<z<-1.5) The area between z = -2 and z = -1.5 is 0.0440 S7

36. Case No. 4 1. Find the area between z = -1.32 and z = 2.37 Steps Solution S1 S2 S3 S4 S5 z = -1.32 corresponds to an area of 0.4066 z = 2.37 corresponds to an area of 0.4911

37. Steps Solution S6 The graph suggests addition The required area is equal to = 0.4066 + 0.4911 = 0.8977 P(-1.32<z<2.37) The area between z = -2 and z = -1.5 is 0.8977 S7

38. Find the area of the following z – values: 1. between z = -0.98 and z = 2.58 2. between z = 1.92 and z = 2.75 Individual 9:

39. Answers: 1. Find the area between z = -0.98 and z = 2.58 Steps Solution S1 S2 S3 S4 S5 z = 0.98 corresponds to an area of 0.3365 z = 2.58 corresponds to an area of 0.4951

40. Steps Solution S6 The graph suggests addition The required area is equal to = 0.3365 + 0.4951 = 0.8316 P(-0.98<z<2.58) The area between z = -0.98 and z = 2.58 is 0.8316 S7

41. 2. Find the area between z = 1.92 and z = 2.75 Steps Solution S1 S2 S3 S4 S5 z = 1.92 corresponds to an area of 0.4726 z = 2.75 corresponds to an area of 0.4970

42. Steps Solution S6 The graph suggests subtraction The required area is equal to = 0.4726 - 0.4970 = - 0.0244 P(1.92<z<2.75) The area between z = 1.92 and z = 2.75 is 0.0244 S7 = 0.0244

43. Find the area of the following z – values: 1. between z = -0.57 and z = 0.07 2. between z = -2.12 and z = 0.89 Quiz 9:

44. Answers: 1. Find the area between z = -0.57 and z = 0.07 Steps Solution S1 S2 S3 S4 S5 z = -0.57 corresponds to an area of 0.2157 z = 0.07 corresponds to an area of 0.0279

45. Steps Solution S6 The graph suggests subtraction The required area is equal to = 0.2157 - 0.0279 = 0.1878 P(-0.57<z<0.07) The area between z = -0.57 and z = 0.07 is 0.1878 S7

46. 2. Find the area between z = -2.12 and z = 0.89 Steps Solution S1 S2 S3 S4 S5 z = -2.12 corresponds to an area of 0.4830 z = 0.89 corresponds to an area of 0.3133

47. Steps Solution S6 The graph suggests addition The required area is equal to = 0.4830 + 0.3133 = 0. 7963 P(-2.12<z<0.89) The area between z = -2.12 and z = 0.89 is 0.7963 S7 = 0.7963

48. Assignment Study on how to compute the percentile under the normal curve.