it all comes out in the washers

It All Comes OutIn the Washers

PhET Interactive SimulationsUniversity of Coloradohttp://phet.colorado.edu

Created byBrian Domroes

It All Comes Out in the Washers

We will learn about…• Mathematics in Engineering

We will learn about…• Normal Distributions

http://encefalus.com/philosophical/logic/

http://encefalus.com/philosophical/logic/

We will learn about…• Standard Deviation

http://encefalus.com/philosophical/logic/

We will learn about…• Z scores

Model Search• Ideal Height is 5’9”

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Ideal and Limits5’6”

6’

5’9”

Women’s Height

1 standard deviation below

64.4” – 2.4” = 62”

34% 62” – 64.4”

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Random Sample

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Women’s Height

Standard Deviation 2.4”

Mean is 64.4”

Good Fit?

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Women’s Height

Standard Deviation 2.4”

Mean is 64.4”5’6”

6’

5’9”

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

Height Data

Recording Data

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Did our data look like this?

XX XX

X XX XX

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XXX

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XX

X

Results – 100 Trials

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Results – 500 Trials

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Results – 10,000 Trials

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5’6”

6’

5’9”Mean 70.7”Median 70”Standard Deviation 3.16”

Does Group A fit criteria?

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5’6”

6’

5’9”Mean 67.8”Median 68”Standard Deviation 2.91”

Does Group B fit criteria?

Combined Samples

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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”

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Standard Deviation Ordering

A B

C

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Answer

Which is which?

The swimmers must be…..hmm?

Standard Deviation 2.91”Mean 67.8”

Standard Deviation 3.16”Mean 70.7”

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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

Z scores• Shows % within limits

Determining Percent

http://encefalus.com/philosophical/logic/

Z Score Calculations

What % fits height limits?

Standard Deviation 2.91”

Mean is 67.8”

Lower height limit 66”

Upper height limit 72”

Swimmer Data

5 a)

What % fits height limits?

Standard Deviation 2.91”

Mean is 67.8”

Lower height limit 66”

Upper height limit 72”

Swimmer Data

5 b)

65.7% of Swimmers

72 “66 “

z = -.619 z = 1.443

What % fits data?

Standard Deviation 3.16”

Mean is 70.7”

Lower height limit 66”

Upper height limit 72”

Basketball Data

59.1% of Basketball

72 “66 “

z = -1.487 z = .411

More Swimmers in Limits

65.7% 59.1%

Division 1 Swimmers Division 1 Basketball

Manufacturing

Presence of Error• Human• Random

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Manufacturing

Voice of the Process

Mean

6

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Customer’s Needs

Voice of Customer

Lower specification

limit

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Upperspecification

limit

Washer Activity

Responsibilities Set 1• Weighing Washers

Responsibilities Set 2• Arranging Washers

Responsibilities Set 3• Input Data

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Observations

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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

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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

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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

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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

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Comparing Standard Deviation

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5 grams 6 grams

Fastenal Washers Sales Washers

Comparing Your Data

Fastenal WashersMean 4.278

Standard Deviation .096

Sales WashersMean 6.124

Standard Deviation .071

Voice of the Process

Fastenal Washers

Sales Washers

Business Proposals• Pretend that you are the washer manufactures

BMW and Lowes

How many washers?• Weight – 6.08 g to 6.18 g

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What Sales is capable of making

Z scores• What percent is good?

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Determining Percent

http://encefalus.com/philosophical/logic/

Z Score Calculations

Z Score Calculations

Round to the nearest thousandth

BMW Z score Lower Limit

= 6.08 – 6.124.071

≈ -.6201

BMW Z score Upper Limit

= 6.18 – 6.124.071

≈ .7892

BMW Probability• 51.7% washers in range

z ≈ -.620 Z ≈ .789a.

Lowe’s Z Score Calculation

Lowe’s Z score Lower Limit

= 4.20 – 4.278.096

≈ -.8131

Lowe’s Z score Upper Limit

= 4.41 – 4.278.096

≈ 1.3752

Lowe’s Probability• 70.7% washers in range

z ≈ -.813 z ≈ 1.375a.

Top Quality

Cost/Benefit Analysis