It All Comes Out In the Washers
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It All Comes OutIn the Washers
PhET Interactive SimulationsUniversity of Coloradohttp://phet.colorado.edu
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Created byBrian Domroes
It All Comes Out in the Washers
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We will learn about…• Mathematics in Engineering
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We will learn about…• Normal Distributions
http://encefalus.com/philosophical/logic/
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http://encefalus.com/philosophical/logic/
We will learn about…• Standard Deviation
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http://encefalus.com/philosophical/logic/
We will learn about…• Z scores
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Model Search• Ideal Height is 5’9”
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48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78
Ideal and Limits5’6”
6’
5’9”
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Women’s Height
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1 standard deviation below
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64.4” – 2.4” = 62”
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34% 62” – 64.4”
http://encefalus.com/philosophical/logic/http://encefalus.com/philosophical/logic/
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Random Sample
48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78
Women’s Height
Standard Deviation 2.4”
Mean is 64.4”
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Good Fit?
48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78
Women’s Height
Standard Deviation 2.4”
Mean is 64.4”5’6”
6’
5’9”
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Where Should I Look?• 3 different groups–Your class–Group A–Group B
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Height Data
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Recording Data
1
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Did our data look like this?
XX XX
X XX XX
X
X
XX
XX
XX X
XXX
X
X
XX
X
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Results – 100 Trials
www.shodor.org
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Results – 500 Trials
www.shodor.org
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Results – 10,000 Trials
www.shodor.org
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49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79More
0
1
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10
5’6”
6’
5’9”Mean 70.7”Median 70”Standard Deviation 3.16”
Does Group A fit criteria?
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49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79More
0
1
2
3
4
5
6
7
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5’6”
6’
5’9”Mean 67.8”Median 68”Standard Deviation 2.91”
Does Group B fit criteria?
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Combined Samples
49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79More
0
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2
3
4
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10
D 1 SwimmersD 1 Basketball
Both
Standard Deviation 2.91”Mean 67.8”
Standard Deviation 3.16”Mean 70.7”
5’6”
6’
5’9”
2
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Standard Deviation Ordering
A B
C
3
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Answer
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Which is which?
The swimmers must be…..hmm?
Standard Deviation 2.91”Mean 67.8”
Standard Deviation 3.16”Mean 70.7”
4
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And the answer is..Standard Deviation 2.91”Mean 67.8”
Standard Deviation 3.16”Mean 70.7”
D 1 Swimmers D 1 Basketball
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Z scores• Shows % within limits
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Determining Percent
http://encefalus.com/philosophical/logic/
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Z Score Calculations
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What % fits height limits?
Standard Deviation 2.91”
Mean is 67.8”
Lower height limit 66”
Upper height limit 72”
Swimmer Data
5 a)
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What % fits height limits?
Standard Deviation 2.91”
Mean is 67.8”
Lower height limit 66”
Upper height limit 72”
Swimmer Data
5 b)
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65.7% of Swimmers
72 “66 “
z = -.619 z = 1.443
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What % fits data?
Standard Deviation 3.16”
Mean is 70.7”
Lower height limit 66”
Upper height limit 72”
Basketball Data
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59.1% of Basketball
72 “66 “
z = -1.487 z = .411
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More Swimmers in Limits
65.7% 59.1%
Division 1 Swimmers Division 1 Basketball
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Manufacturing
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Presence of Error• Human• Random
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http://encefalus.com/philosophical/logic/
Manufacturing
Voice of the Process
Mean
6
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http://encefalus.com/philosophical/logic/
Customer’s Needs
Voice of Customer
Lower specification
limit
7
Upperspecification
limit
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Washer Activity
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Responsibilities Set 1• Weighing Washers
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Responsibilities Set 2• Arranging Washers
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Responsibilities Set 3• Input Data
8
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Observations
9
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200 Fastenal Washers
3.75 - 3.85 3.86 - 3.96 3.97 - 4.07 4.08 - 4.18 4.19 - 4.29 4.30 - 4.40 4.41 - 4.51 More0
20
40
60
80
100
120
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Fastenal Washers per Weight
3.753.78
3.813.84
3.87 3.93.93
3.963.99
4.024.05
4.084.11
4.144.17 4.2
4.234.26
4.294.32
4.354.38
4.414.44
4.47 4.50
5
10
15
20
25
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200 Sales Washers
5.87 - 5.92 5.93 - 5.98 5.99 - 6.04 6.05 - 6.1 6.11 - 6.16 6.17 - 6.22 6.23 - 6.28 More0
10
20
30
40
50
60
70
80
90
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Sales Washers per Weight
5.875.89
5.915.93
5.955.97
5.996.01
6.036.05
6.076.09
6.116.13
6.156.17
6.196.21
6.236.25
0
2
4
6
8
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12
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16
18
20
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Comparing Standard Deviation
10
5 grams 6 grams
Fastenal Washers Sales Washers
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Comparing Your Data
Fastenal WashersMean 4.278
Standard Deviation .096
Sales WashersMean 6.124
Standard Deviation .071
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Voice of the Process
Fastenal Washers
Sales Washers
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Business Proposals• Pretend that you are the washer manufactures
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BMW and Lowes
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How many washers?• Weight – 6.08 g to 6.18 g
0
2
4
6
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10
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16
18
20Range BMW will accept
What Sales is capable of making
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Z scores• What percent is good?
0
2
4
6
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12
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18
20
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Determining Percent
http://encefalus.com/philosophical/logic/
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Z Score Calculations
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Z Score Calculations
Round to the nearest thousandth
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BMW Z score Lower Limit
= 6.08 – 6.124.071
≈ -.6201
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BMW Z score Upper Limit
= 6.18 – 6.124.071
≈ .7892
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BMW Probability• 51.7% washers in range
z ≈ -.620 Z ≈ .789a.
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Lowe’s Z Score Calculation
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Lowe’s Z score Lower Limit
= 4.20 – 4.278.096
≈ -.8131
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Lowe’s Z score Upper Limit
= 4.41 – 4.278.096
≈ 1.3752
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Lowe’s Probability• 70.7% washers in range
z ≈ -.813 z ≈ 1.375a.
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Top Quality
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Cost/Benefit Analysis
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