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 Limits

5’6”

6’

5’9”

Women’s Height

1 standard deviation below

64.4” – 2.4” = 62”

34% 62” – 64.4”

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

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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X

Results – 100 Trials

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Results – 500 Trials

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Results – 10,000 Trials

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ore0

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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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ore0

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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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ore0

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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”

4

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

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

Manufacturing

Voice of the Process

Mean

6

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

Customer’s Needs

Voice of Customer

Lower specification

limit

7

Upperspecification

limit

Washer Activity

Responsibilities Set 1

• Weighing Washers

Responsibilities Set 2

• Arranging Washers

Responsibilities Set 3

• Input Data

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Observations

9

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

10

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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20Range BMW will accept

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

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