It All Comes Out In the Washers

1. It All Comes OutIn the Washers PhET Interactive Simulations University of Colorado http://phet.colorado.edu

2. It All Comes Out in the Washers Created by Brian Domroes

3. We will learn about… • Mathematics in Engineering

4. We will learn about… • Normal Distributions http://encefalus.com/philosophical/logic/

5. We will learn about… • Standard Deviation http://encefalus.com/philosophical/logic/

6. We will learn about… • Z scores http://encefalus.com/philosophical/logic/

7. Model Search • Ideal Height is 5’9”

8. Ideal and Limits 5’6” 5’9” 6’

9. Women’s Height

10. 1 standard deviation below

11. 64.4” – 2.4” = 62”

12. 34% 62” – 64.4” http://encefalus.com/philosophical/logic/ http://encefalus.com/philosophical/logic/

13. Random Sample Women’s Height Mean is 64.4” Standard Deviation 2.4”

14. Good Fit? Women’s Height 5’9” 5’6” Mean is 64.4” Standard Deviation 2.4” 6’

15. Where Should I Look? • 3 different groups • Your class • Group A • Group B

16. Height Data

17. Recording Data 1

18. Did our data look like this? X X X X X X X X X X X X X X X X X X X X X X X X X X

19. Results – 100 Trials www.shodor.org

20. Results – 500 Trials www.shodor.org

21. Results – 10,000 Trials www.shodor.org

22. Does Group A fit criteria? 5’6” 5’9” Mean 70.7” Median 70” Standard Deviation 3.16” 6’

23. Does Group B fit criteria? 5’6” 5’9” Mean 67.8” Median 68” Standard Deviation 2.91” 6’

24. Combined Samples 5’6” 5’9” Standard Deviation 2.91” Mean 67.8” Standard Deviation 3.16” Mean 70.7” 6’ 2

25. Standard Deviation Ordering B A C 3

26. Answer

27. Which is which? Standard Deviation 2.91” Mean 67.8” Standard Deviation 3.16” Mean 70.7” The swimmers must be…..hmm? 4

28. And the answer is.. Standard Deviation 2.91” Mean 67.8” Standard Deviation 3.16” Mean 70.7” D 1 Basketball D 1 Swimmers

29. Z scores • Shows % within limits

30. Determining Percent http://encefalus.com/philosophical/logic/

31. Z Score Calculations

32. What % fits height limits? Swimmer Data Mean is 67.8” Standard Deviation 2.91” Lower height limit 66” Upper height limit 72” 5 a)

33. What % fits height limits? Swimmer Data Mean is 67.8” Standard Deviation 2.91” Lower height limit 66” Upper height limit 72” 5 b)

34. 65.7% of Swimmers 72 “ 66 “ z = 1.443 z = -.619

35. What % fits data? Basketball Data Mean is 70.7” Standard Deviation 3.16” Lower height limit 66” Upper height limit 72”

36. 59.1% of Basketball 72 “ 66 “ z = .411 z = -1.487

37. More Swimmers in Limits Division 1 Basketball Division 1 Swimmers 65.7% 59.1%

38. Manufacturing

39. Presence of Error • Human • Random

40. Manufacturing Mean Voice of the Process http://encefalus.com/philosophical/logic/ 6

41. Customer’s Needs Upper specification limit Lower specification limit Voice of Customer http://encefalus.com/philosophical/logic/ 7

42. Washer Activity

43. Responsibilities Set 1 • Weighing Washers

44. Responsibilities Set 2 • Arranging Washers

45. Responsibilities Set 3 • Input Data 8

46. Observations 9

47. 200 Fastenal Washers

48. Fastenal Washers per Weight

49. 200 Sales Washers

50. Sales Washers per Weight