BELL GRAPH

7/28/2019 BELL GRAPH

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Continuous Probability Distribution

Uniform Probability Distribution

Normal Probability Distribution

Standard Normal Probability Distribution

NORMDIST Excel function

NORMINV Excel function

NORMSDIST Excel functionNORMSINV Excel function

Exponential Probability Distribution

EXPONDIST Excel function

Relationship between Poisson and Exponential Probability Distributions


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n 10 Binomial Distribution, n = 10 p = 0.5 P(X


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Test Score Category Frequency

0 10 0 up to 10 1

10 20 10 up to 20 2

20 30 20 up to 30 3

30 40 30 up to 40 10

40 50 40 up to 50 12

50 60 50 up to 60 1560 70 60 up to 70 18

70 80 70 up to 80 22

80 90 80 up to 90 15

90 100 90 up to 100 2

100

Test Score Category Frequency

0 10 0 up to 10 10

10 20 10 up to 20 10

20 30 20 up to 30 10

30 40 30 up to 40 10

40 50 40 up to 50 1050 60 50 up to 60 10

60 70 60 up to 70 10

70 80 70 up to 80 10

80 90 80 up to 90 10

90 100 90 up to 100 10

100

1 23

1012

15

18

22

15

2

0 up to

10

10 up

to 20

20 up

to 30

30 up

to 40

40 up

to 50

50 up

to 60

60 up

to 70

70 up

to 80

80 up

to 90

90 up

to 100

Test Score Category

Quiz 4

10 10 10 10 10 10 10 10 10 10

0

5

10

15

20

0 up

to 10

10 up

to 20

20 up

to 30

30 up

to 40

40 up

to 50

50 up

to 60

60 up

to 70

70 up

to 80

80 up

to 90

90 up

to 100

Test Score Category

Quiz 4


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x

) = 1/(b-a)

have no area


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Driving Distance for the top 100 golfers on the PGA tour

(2003)

Distribution is Uniform

Lower 284.7 yards

Upper 310.6 yards

Difference = width yards

Probability Density function of driving distances:

F(x) = 1/(310.6-284.7) = 1/25.9

for interval 284.7


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310.6 x

310.6 x

x


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Driving Distance for the top 100 golfers on the PGA tour

(2003)

Distribution is Uniform

Lower 284.7 yards f(x)

Upper 310.6 yards 1/25.9

Difference = width 25.9 yards

Probability Density function of driving distances:

F(x) = 1/(310.6-284.7) = 1/25.9

for interval 284.7


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310.6 x

310.6 x

310.6 x

x


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Past Quiz Results

(Population Data) for

Chapter 5 (Probability) Mean = mu = 12.00 label X = Score

12 Median 12.00 0 up to 1 1

14 Mode 12.00 1 up to 2 2

14 Skew 0.00 2 up to 3 3

12 SD = sigma = 2.00 3 up to 4 418 4 up to 5 5

17 Mean = mu = = 12 5 up to 6 6

17 Median = 12 6 up to 7 7

12 Mode = 12 7 up to 8 8

11 Skew = 0 8 up to 9 9

12 SD = sigma = = 2 9 up to 10 10

13 Mean = mu = = 12Median = 12Mo 10 up to 11 11

12 11 up to 12 12

10 12 up to 13 13

12 13 up to 14 14

14 14 up to 15 15

12 15 up to 16 16

6 16 up to 17 17

13 17 up to 18 18

11 18 up to 19 19

13 19 up to 20 20

12

7

11

16

1415

14

15

14

15

14

15

14

12

14

1515

14

15

15

14

14

8

12

0

0.05

0.1

0.15

0.2

0.25

0 up

to 1

1 up

to 2

2 up

to 3

3 up

to 4

4 up

to 5

5 up

to 6

6 up

to 7

7 up

to 8

8 up

to 9

9 up

to 10

10 up

to 11

11 up

to 12

12 up

to 13

13 up

to 14

14 up

to 15

15 up

to 16

16 up

to 17

17 up

to 18

18 up

to 19

19 up

to 20

Re

lative

Freq

uency

X = Score

Past Quiz Results (Population Data) for Chapter 5 (Probability)

Mean = mu = = 12

Median = 12

Mode = 12

Skew = 0

SD = sigma = = 2


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12

13

14

16

14

11

109

10

11

11

13

12

9

10

15

11

13

9

13

13

11

9

12

13

12

10

1112

12

11

9

13

10

13

15

11

8

1314

12

12

9

12

9

9

9


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Frequency

Relative

Frequency YforLine XforLine mean 12

0 0 0 0 SD 2

0 0 0 3.5

0 0 0 4.5

0 0 0 5.50 0 0 6.5

1 0.006060606 0 7.5

2 0.012121212 0.006060606 8.5

3 0.018181818 0.012121212 9.5

14 0.084848485 0.018181818 10.5

18 0.109090909 0.084848485 11.5

26 0.157575758 0.109090909 12.5

37 0.224242424 0.157575758 13.5

26 0.157575758 0.224242424 14.5

18 0.109090909 0.157575758 15.5

14 0.084848485 0.109090909 16.5

3 0.018181818 0.084848485 17.5

2 0.012121212 0.018181818 18.5

1 0.006060606 0.012121212 19.5

0 0 0.006060606 20.5

0 0 0 21.5

165 0 22.5

0 23.5


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X = Score

Relative

Frequency

0 0

0.1 0

0.2 0

0.3 00.4 0

0.5 0

0.6 0

0.7 0

0.8 0

0.9 0

1 0

1.1 0

1.2 0

1.3 0

1.4 0

1.5 0

1.6 0

1.7 0

1.8 0

1.9 0

2 0

2.1 0

2.2 0

2.3 0

2.4 02.5 0

2.6 0

2.7 0

2.8 0

2.9 0

3 0

3.1 0

3.2 0

3.3 0

3.4 0

3.5 03.6 0

3.7 0

3.8 0

3.9 0

4 0

4.1 0

4.2 0

4.3 0


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4.4 0

4.5 0

4.6 0

4.7 0

4.8 0

4.9 0

5 05.1 0

5.2 0

5.3 0

5.4 0

5.5 0.006061

5.6 0.006061

5.7 0.006061

5.8 0.006061

5.9 0.006061

6 0.006061

6.1 0.006061

6.2 0.006061

6.3 0.006061

6.4 0.006061

6.5 0.012121

6.6 0.012121

6.7 0.012121

6.8 0.012121

6.9 0.012121

7 0.012121

7.1 0.0121217.2 0.012121

7.3 0.012121

7.4 0.012121

7.5 0.018182

7.6 0.018182

7.7 0.018182

7.8 0.018182

7.9 0.018182

8 0.018182

8.1 0.018182

8.2 0.0181828.3 0.018182

8.4 0.018182

8.5 0.084848

8.6 0.084848

8.7 0.084848

8.8 0.084848

8.9 0.084848

9 0.084848


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x = Test Scores 13

mean = 12

SD = 1

mean = = 12. SD = = 1.

# SD 5

12 - 5*1 7

12 + 5*1 17Position of 7 in list 71

Position of 17 in list 171

Height of curve

x = Test Score Remaining Area = 15.8655% X


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7 1.48672E-06 1.48672E-06

7.1 2.43896E-06 2.43896E-06

7.2 3.9613E-06 3.9613E-06

7.3 6.36983E-06 6.36983E-067.4 1.01409E-05 1.01409E-05

7.5 1.59837E-05 1.59837E-05

7.6 2.49425E-05 2.49425E-05

7.7 3.85352E-05 3.85352E-05

7.8 5.89431E-05 5.89431E-05

7.9 8.92617E-05 8.92617E-05

8 0.00013383 0.00013383

8.1 0.000198655 0.000198655


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12.9 0.26608525 0.26608525

13 0.241970725 0.241970725

13.1 0.217852177

13.2 0.194186055

13.3 0.171368592

13.4 0.149727466

13.5 0.12951759613.6 0.110920835

13.7 0.094049077

13.8 0.078950158

13.9 0.065615815

14 0.053990967

14.1 0.043983596

14.2 0.035474593

14.3 0.028327038

14.4 0.02239453

14.5 0.0175283

14.6 0.013582969

14.7 0.010420935

14.8 0.007915452

14.9 0.005952532

15 0.004431848

15.1 0.003266819

15.2 0.002384088

15.3 0.001722569

15.4 0.001232219

15.5 0.000872683

15.6 0.00061190215.7 0.00042478

15.8 0.000291947

15.9 0.000198655

16 0.00013383

16.1 8.92617E-05

16.2 5.89431E-05

16.3 3.85352E-05

16.4 2.49425E-05

16.5 1.59837E-05

16.6 1.01409E-05

16.7 6.36983E-0616.8 3.9613E-06

16.9 2.43896E-06

17 1.48672E-06


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X z Height X


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11.6 -0.4 0.36827014 0.36827014

11.7 -0.3 0.38138782 0.38138782

11.8 -0.2 0.39104269 0.39104269

11.9 -0.1 0.39695255 0.39695255

12 0 0.39894228 0.39894228

12.1 0.1 0.39695255 0.39695255

12.2 0.2 0.39104269 0.3910426912.3 0.3 0.38138782 0.38138782

12.4 0.4 0.36827014 0.36827014

12.5 0.5 0.35206533 0.35206533

12.6 0.6 0.3332246 0.3332246

12.7 0.7 0.31225393 0.31225393

12.8 0.8 0.28969155 0.28969155

12.9 0.9 0.26608525 0.26608525

13 1 0.24197072

13.1 1.1 0.21785218

13.2 1.2 0.19418605

13.3 1.3 0.17136859

13.4 1.4 0.14972747

13.5 1.5 0.1295176

13.6 1.6 0.11092083

13.7 1.7 0.09404908

13.8 1.8 0.07895016

13.9 1.9 0.06561581

14 2 0.05399097

14.1 2.1 0.0439836

14.2 2.2 0.03547459

14.3 2.3 0.0283270414.4 2.4 0.02239453

14.5 2.5 0.0175283

14.6 2.6 0.01358297

14.7 2.7 0.01042093

14.8 2.8 0.00791545

14.9 2.9 0.00595253

15 3 0.00443185

15.1 3.1 0.00326682

15.2 3.2 0.00238409

15.3 3.3 0.00172257

15.4 3.4 0.0012322215.5 3.5 0.00087268

15.6 3.6 0.0006119

15.7 3.7 0.00042478

15.8 3.8 0.00029195

15.9 3.9 0.00019866

16 4 0.00013383

16.1 4.1 8.9262E-05

16.2 4.2 5.8943E-05


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16.3 4.3 3.8535E-05

16.4 4.4 2.4942E-05

16.5 4.5 1.5984E-05

16.6 4.6 1.0141E-05

16.7 4.7 6.3698E-06

16.8 4.8 3.9613E-06

16.9 4.9 2.439E-0617 5 1.4867E-06


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11

.5

12

12

.5

13

13

.5

14

14

.5

15

15

.5

16

16

.5

17

howing Both X and Z (scores)

Height

X


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11 -0.5 0.176032663

11.2 -0.4 0.18413507

11.4 -0.3 0.190693908

11.6 -0.2 0.195521347

11.8 -0.1 0.198476274

12 0 0.19947114

12.2 0.1 0.19847627412.4 0.2 0.195521347

12.6 0.3 0.190693908

12.8 0.4 0.18413507

13 0.5 0.176032663

13.2 0.6 0.166612301

13.4 0.7 0.156126967

13.6 0.8 0.144845776

13.8 0.9 0.133042625

14 1 0.120985362

14.2 1.1 0.108926089

14.4 1.2 0.097093027

14.6 1.3 0.085684296

14.8 1.4 0.074863733

15 1.5 0.064758798

15.2 1.6 0.055460417

15.4 1.7 0.047024539

15.6 1.8 0.039475079

15.8 1.9 0.032807907

16 2 0.026995483

16.2 2.1 0.021991798

16.4 2.2 0.01773729616.6 2.3 0.014163519

16.8 2.4 0.011197265

17 2.5 0.00876415

17.2 2.6 0.006791485

17.4 2.7 0.005210467

17.6 2.8 0.003957726

17.8 2.9 0.002976266

18 3 0.002215924

18.2 3.1 0.00163341

18.4 3.2 0.001192044

18.6 3.3 0.00086128418.8 3.4 0.00061611

19 3.5 0.000436341

19.2 3.6 0.000305951

19.4 3.7 0.00021239

19.6 3.8 0.000145973

19.8 3.9 9.93277E-05

20 4 6.69151E-05

20.2 4.1 4.46308E-05


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20.4 4.2 2.94715E-05

20.6 4.3 1.92676E-05

20.8 4.4 1.24712E-05

21 4.5 7.99187E-06

21.2 4.6 5.07043E-06

21.4 4.7 3.18491E-06

21.6 4.8 1.98065E-0621.8 4.9 1.21948E-06

22 5 7.4336E-07


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x = actual test score

z = Standard Normal Random Variable = # of

standard Deviations away from mean


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3

3.1

3.2

3.3

3.4

3.5

3.63.7

3.8

3.9

4

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

4.9

5

5.1

5.2

5.3

5.4

5.5

5.6

5.75.8

5.9

6

6.1

6.2

6.3

6.4

6.5

6.6

6.7

6.86.9

7

7.1

7.2

7.3

7.4

7.5

7.6


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7.7

7.8

7.9

8

8.1

8.2

8.38.4

8.5

8.6

8.7

8.8

8.9

9

9.1

9.2

9.3

9.4

9.5

9.6

9.7

9.8

9.9

10

10.1

10.2

10.3

10.410.5

10.6

10.7

10.8

10.9

11

11.1

11.2

11.3

11.4

11.511.6

11.7

11.8

11.9

12

12.1

12.2

12.3


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remaining

area 1

Area for


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Based on past data, estimate the percentage of scores on the next statistics test that will be 10 or

less.

Test Score x 14

Operator 1


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3 7.99187E-06

3.1 9.9959E-06

3.2 1.24712E-05

3.3 1.55207E-05

3.4 1.92676E-05

3.5 2.38593E-05

3.6 2.94715E-053.7 3.6313E-05

3.8 4.46308E-05

3.9 5.4717E-05

4 6.69151E-05

4.1 8.16282E-05

4.2 9.93277E-05

4.3 0.000120563

4.4 0.000145973

4.5 0.000176298

4.6 0.00021239

4.7 0.000255232

4.8 0.000305951

4.9 0.000365832

5 0.000436341

5.1 0.000519141

5.2 0.00061611

5.3 0.000729365

5.4 0.000861284

5.5 0.001014524

5.6 0.001192044

5.7 0.0013971295.8 0.00163341

5.9 0.001904881

6 0.002215924

6.1 0.00257132

6.2 0.002976266

6.3 0.003436383

6.4 0.003957726

6.5 0.004546781

6.6 0.005210467

6.7 0.005956122

6.8 0.0067914856.9 0.007724674

7 0.00876415

7.1 0.009918677

7.2 0.011197265

7.3 0.01260911

7.4 0.014163519

7.5 0.015869826

7.6 0.017737296


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7.7 0.019775021

7.8 0.021991798

7.9 0.024396009

8 0.026995483

8.1 0.029797353

8.2 0.032807907

8.3 0.0360324378.4 0.039475079

8.5 0.043138659

8.6 0.047024539

8.7 0.051132462

8.8 0.055460417

8.9 0.0600045

9 0.064758798

9.1 0.069715283

9.2 0.074863733

9.3 0.080191664

9.4 0.085684296

9.5 0.091324543

9.6 0.097093027

9.7 0.102968134

9.8 0.108926089

9.9 0.11494107

10 0.120985362

10.1 0.127029528

10.2 0.133042625

10.3 0.138992443

10.4 0.14484577610.5 0.150568716

10.6 0.156126967

10.7 0.16148618

10.8 0.166612301

10.9 0.171471928

11 0.176032663

11.1 0.180263481

11.2 0.18413507

11.3 0.187620173

11.4 0.190693908

11.5 0.19333405811.6 0.195521347

11.7 0.197239665

11.8 0.198476274

11.9 0.199221957

12 0.19947114

12.1 0.199221957

12.2 0.198476274

12.3 0.197239665


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12.4 0.195521347

12.5 0.193334058

12.6 0.190693908

12.7 0.187620173

12.8 0.18413507

12.9 0.180263481

13 0.17603266313.1 0.171471928

13.2 0.166612301

13.3 0.16148618

13.4 0.156126967

13.5 0.150568716

13.6 0.144845776

13.7 0.138992443

13.8 0.133042625

13.9 0.127029528

14 0.120985362

14.1 0.11494107

14.2 0.108926089

14.3 0.102968134

14.4 0.097093027

14.5 0.091324543

14.6 0.085684296

14.7 0.080191664

14.8 0.074863733

14.9 0.069715283

15 0.064758798

15.1 0.060004515.2 0.055460417

15.3 0.051132462

15.4 0.047024539

15.5 0.043138659

15.6 0.039475079

15.7 0.036032437

15.8 0.032807907

15.9 0.029797353

16 0.026995483

16.1 0.024396009

16.2 0.02199179816.3 0.019775021

16.4 0.017737296

16.5 0.015869826

16.6 0.014163519

16.7 0.01260911

16.8 0.011197265

16.9 0.009918677

17 0.00876415


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remaining

area 0.158655

Area for


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7.99187E-06

9.9959E-06

1.24712E-05

1.55207E-05

1.92676E-05

2.38593E-05

2.94715E-053.6313E-05

4.46308E-05

5.4717E-05

6.69151E-05

8.16282E-05

9.93277E-05

0.000120563

0.000145973

0.000176298

0.00021239

0.000255232

0.000305951

0.000365832

0.000436341

0.000519141

0.00061611

0.000729365

0.000861284

0.001014524

0.001192044

0.0013971290.00163341

0.001904881

0.002215924

0.00257132

0.002976266

0.003436383

0.003957726

0.004546781

0.005210467

0.005956122

0.0067914850.007724674

0.00876415

0.009918677

0.011197265

0.01260911

0.014163519

0.015869826

0.017737296


231/331

0.019775021

0.021991798

0.024396009

0.026995483

0.029797353

0.032807907

0.0360324370.039475079

0.043138659

0.047024539

0.051132462

0.055460417

0.0600045

0.064758798

0.069715283

0.074863733

0.080191664

0.085684296

0.091324543

0.097093027

0.102968134

0.108926089

0.11494107

0.120985362

0.127029528

0.133042625

0.138992443

0.1448457760.150568716

0.156126967

0.16148618

0.166612301

0.171471928

0.176032663

0.180263481

0.18413507

0.187620173

0.190693908

0.1933340580.195521347

0.197239665

0.198476274

0.199221957

0.19947114

0.199221957

0.198476274

0.197239665


232/331

0.195521347

0.193334058

0.190693908

0.187620173

0.18413507

0.180263481

0.1760326630.171471928

0.166612301

0.16148618

0.156126967

0.150568716

0.144845776

0.138992443

0.133042625

0.127029528

0.120985362


233/331


234/331

Based on past data, estimate the percentage of scores on the next statistics test that will be 15 or more.

What should we do if 37% get a score of 15 or more?

Test Score x 15

Operator 1 >= Test Score = mean = mu = = 12, s

Operator 2

Test Score = mean = mu = = 12

standard deviation = sigma = = 2Z

p(X >= 15) =1-NORMDIST(C2,C5,C6,1)

p(Z >= ) =1-NORMSDIST(C7)

What is x given cumulative Probability? =NORMINV(1-C8,C5,C6)

What is z given cumulative Probability? =NORMSINV(1-C9)

Height of curve

x = Test Score Remaining Area

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

11.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

2.12.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

Note: Because we are dealing with

continuous random variables and we are

calculating probability from area and

because the area of a line is zero, P(>=15) =

P(>15)


235/331


236/331

7.7

7.8

7.9

8

8.1

8.2

8.38.4

8.5

8.6

8.7

8.8

8.9

9

9.1

9.2

9.3

9.4

9.5

9.6

9.7

9.8

9.9

10

10.1

10.2

10.3

10.410.5

10.6

10.7

10.8

10.9

11

11.1

11.2

11.3

11.4

11.511.6

11.7

11.8

11.9

12

12.1

12.2

12.3


237/331

12.4

12.5

12.6

12.7

12.8

12.9

1313.1

13.2

13.3

13.4

13.5

13.6

13.7

13.8

13.9

14

14.1

14.2

14.3

14.4

14.5

14.6

14.7

14.8

14.9

15

15.115.2

15.3

15.4

15.5

15.6

15.7

15.8

15.9

16

16.1

16.216.3

16.4

16.5

16.6

16.7

16.8

16.9

17


238/331

17.1

17.2

17.3

17.4

17.5

17.6

17.717.8

17.9

18

18.1

18.2

18.3

18.4

18.5

18.6

18.7

18.8

18.9

19

19.1

19.2

19.3

19.4

19.5

19.6

19.7

19.819.9

20

Total is not 1 because not Probability 0


239/331

andard deviation = sigma = = 2

Area for>=15

F17 has the formula:

=NORMDIST(E17,$C$5,$C$6,0)

G17 has the formula:

=IF(E17>=$C$2,F17,"")


240/331


241/331


242/331


243/331


244/331

Based on past data, estimate the percentage of scores on the next statistics test that will be 15 or more.

What should we do if 37% get a score of 15 or more?

Test Score x 15

Operator 1 >= Score = mean = mu = = 12, stand

Operator 2

Score = mean = mu = = 12

standard deviation = sigma = = 2Z 1.5

p(X >= 15) 0.066807 =1-NORMDIST(C2,C5,C6,1)

p(Z >= 1.5) 0.066807 =1-NORMSDIST(C7)

What is x given cumulative Probability? 15 =NORMINV(1-C8,C5,C6)

What is z given cumulative Probability? 1.5 =NORMSINV(1-C9)

Height of curve

x = Test Score Remaining Area

0 3.03794E-09

0.1 4.09567E-09

0.2 5.50788E-09

0.3 7.38854E-09

0.4 9.8866E-09

0.5 1.31962E-08

0.6 1.75698E-08

0.7 2.33344E-08

0.8 3.09131E-08

0.9 4.0851E-08

1 5.38488E-081.1 7.0805E-08

1.2 9.28681E-08

1.3 1.21502E-07

1.4 1.58567E-07

1.5 2.06424E-07

1.6 2.68052E-07

1.7 3.4721E-07

1.8 4.48622E-07

1.9 5.78206E-07

2 7.4336E-07

2.1 9.533E-072.2 1.21948E-06

2.3 1.55609E-06

2.4 1.98065E-06

2.5 2.51475E-06

2.6 3.18491E-06

2.7 4.02359E-06

2.8 5.07043E-06

2.9 6.37367E-06

Based on past data it would be

reasonable to assume that 6.68% of all

the scores on the next text will be 15 or

more. If we then run the test and 37% ofthe tests are above 15, we would need

to investigate why.

Note: Because we are dealing with

continuous random variables and we are

calculating probability from area and

because the area of a line is zero, P(>=15) =

P(>15)


245/331

3 7.99187E-06

3.1 9.9959E-06

3.2 1.24712E-05

3.3 1.55207E-05

3.4 1.92676E-05

3.5 2.38593E-05

3.6 2.94715E-053.7 3.6313E-05

3.8 4.46308E-05

3.9 5.4717E-05

4 6.69151E-05

4.1 8.16282E-05

4.2 9.93277E-05

4.3 0.000120563

4.4 0.000145973

4.5 0.000176298

4.6 0.00021239

4.7 0.000255232

4.8 0.000305951

4.9 0.000365832

5 0.000436341

5.1 0.000519141

5.2 0.00061611

5.3 0.000729365

5.4 0.000861284

5.5 0.001014524

5.6 0.001192044

5.7 0.0013971295.8 0.00163341

5.9 0.001904881

6 0.002215924

6.1 0.00257132

6.2 0.002976266

6.3 0.003436383

6.4 0.003957726

6.5 0.004546781

6.6 0.005210467

6.7 0.005956122

6.8 0.0067914856.9 0.007724674

7 0.00876415

7.1 0.009918677

7.2 0.011197265

7.3 0.01260911

7.4 0.014163519

7.5 0.015869826

7.6 0.017737296


246/331

7.7 0.019775021

7.8 0.021991798

7.9 0.024396009

8 0.026995483

8.1 0.029797353

8.2 0.032807907

8.3 0.0360324378.4 0.039475079

8.5 0.043138659

8.6 0.047024539

8.7 0.051132462

8.8 0.055460417

8.9 0.0600045

9 0.064758798

9.1 0.069715283

9.2 0.074863733

9.3 0.080191664

9.4 0.085684296

9.5 0.091324543

9.6 0.097093027

9.7 0.102968134

9.8 0.108926089

9.9 0.11494107

10 0.120985362

10.1 0.127029528

10.2 0.133042625

10.3 0.138992443

10.4 0.14484577610.5 0.150568716

10.6 0.156126967

10.7 0.16148618

10.8 0.166612301

10.9 0.171471928

11 0.176032663

11.1 0.180263481

11.2 0.18413507

11.3 0.187620173

11.4 0.190693908

11.5 0.19333405811.6 0.195521347

11.7 0.197239665

11.8 0.198476274

11.9 0.199221957

12 0.19947114

12.1 0.199221957

12.2 0.198476274

12.3 0.197239665


247/331

12.4 0.195521347

12.5 0.193334058

12.6 0.190693908

12.7 0.187620173

12.8 0.18413507

12.9 0.180263481

13 0.17603266313.1 0.171471928

13.2 0.166612301

13.3 0.16148618

13.4 0.156126967

13.5 0.150568716

13.6 0.144845776

13.7 0.138992443

13.8 0.133042625

13.9 0.127029528

14 0.120985362

14.1 0.11494107

14.2 0.108926089

14.3 0.102968134

14.4 0.097093027

14.5 0.091324543

14.6 0.085684296

14.7 0.080191664

14.8 0.074863733

14.9 0.069715283

15 0.064758798

15.1 0.060004515.2 0.055460417

15.3 0.051132462

15.4 0.047024539

15.5 0.043138659

15.6 0.039475079

15.7 0.036032437

15.8 0.032807907

15.9 0.029797353

16 0.026995483

16.1 0.024396009

16.2 0.02199179816.3 0.019775021

16.4 0.017737296

16.5 0.015869826

16.6 0.014163519

16.7 0.01260911

16.8 0.011197265

16.9 0.009918677

17 0.00876415


248/331

17.1 0.007724674

17.2 0.006791485

17.3 0.005956122

17.4 0.005210467

17.5 0.004546781

17.6 0.003957726

17.7 0.00343638317.8 0.002976266

17.9 0.00257132

18 0.002215924

18.1 0.001904881

18.2 0.00163341

18.3 0.001397129

18.4 0.001192044

18.5 0.001014524

18.6 0.000861284

18.7 0.000729365

18.8 0.00061611

18.9 0.000519141

19 0.000436341

19.1 0.000365832

19.2 0.000305951

19.3 0.000255232

19.4 0.00021239

19.5 0.000176298

19.6 0.000145973

19.7 0.000120563

19.8 9.93277E-0519.9 8.16282E-05

20 6.69151E-05

Total is not 1 because not Probability 9.999715622


249/331

rd deviation = sigma = = 2

Area for>=15

F17 has the formula:

=NORMDIST(E17,$C$5,$C$6,0)

G17 has the formula:

=IF(E17>=$C$2,F17,"")

0

0.05

0.1

0.15

0.2

0.25

0

0.

9

1.

8

2.

7

3.6

4.

5

5.

4

6.

3

7.

2

8.

1 9

9.

9

10.

8

11.

7

12.

6

13.

5

14.

4

15.

3

16.

2

17.

118

18.

9

19.

8

x = Test Score

Score = mean = mu = = 12, standard deviation = sigma = = 2

Remaining Area Area for>=15

Mean = mu = = 12

Median = 12

Mode = 12

Skew = 0

SD = sigma = = 2

0.066807201Mean = mu = = 12

Median = 12

Mode = 12

Skew = 0

SD = sigma = = 2


250/331


251/331


252/331

0.064758798

0.06000450.055460417

0.051132462

0.047024539

0.043138659

0.039475079

0.036032437

0.032807907

0.029797353

0.026995483

0.024396009

0.0219917980.019775021

0.017737296

0.015869826

0.014163519

0.01260911

0.011197265

0.009918677

0.00876415


253/331

0.007724674

0.006791485

0.005956122

0.005210467

0.004546781

0.003957726

0.0034363830.002976266

0.00257132

0.002215924

0.001904881

0.00163341

0.001397129

0.001192044

0.001014524

0.000861284

0.000729365

0.00061611

0.000519141

0.000436341

0.000365832

0.000305951

0.000255232

0.00021239

0.000176298

0.000145973

0.000120563

9.93277E-058.16282E-05

6.69151E-05


254/331

Based on past data, estimate the percentage of scores on the next statistics test that will be between 10

and 14.

Test Score x1 10

x2 14

Operator 1 >=

Operator 2 = x = z =10) =

P(>10)


255/331

2.9

3

3.1

3.2

3.3

3.4

3.53.6

3.7

3.8

3.9

4

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

4.9

5

5.1

5.2

5.3

5.4

5.5

5.65.7

5.8

5.9

6

6.1

6.2

6.3

6.4

6.5

6.6

6.76.8

6.9

7

7.1

7.2

7.3

7.4

7.5


256/331

7.6

7.7

7.8

7.9

8

8.1

8.28.3

8.4

8.5

8.6

8.7

8.8

8.9

9

9.1

9.2

9.3

9.4

9.5

9.6

9.7

9.8

9.9

10

10.1

10.2

10.310.4

10.5

10.6

10.7

10.8

10.9

11

11.1

11.2

11.3

11.411.5

11.6

11.7

11.8

11.9

12

12.1

12.2


257/331

12.3

12.4

12.5

12.6

12.7

12.8

12.913

13.1

13.2

13.3

13.4

13.5

13.6

13.7

13.8

13.9

14

14.1

14.2

14.3

14.4

14.5

14.6

14.7

14.8

14.9

1515.1

15.2

15.3

15.4

15.5

15.6

15.7

15.8

15.9

16

16.116.2

16.3

16.4

16.5

16.6

16.7

16.8

16.9


258/331

17

17.1

17.2

17.3

17.4

17.5

17.617.7

17.8

17.9

18

18.1

18.2

18.3

18.4

18.5

18.6

18.7

18.8

18.9

19

19.1

19.2

19.3

19.4

19.5

19.6

19.719.8

19.9

20

Total is not 1 because not Probability 0


259/331

ST(C2,C6,C7,1)

Area for>=10 and

=$C$2,E17


260/331


261/331


262/331


263/331


264/331

Based on past data, estimate the percentage of scores on the next statistics test that will be between 10

and 14.

Test Score x1 10

x2 14

Operator 1 >=

Operator 2 = x = z =10) =

P(>10)

0

0.05

0.1

0.15

0.2

0.25

0

1.

7

3.

4

5.

1

6.

8

8.

5

10

.2

11

.9

13

.6

15

.3

Test Scores, Mu =


265/331

2.9 6.37367E-06

3 7.99187E-06

3.1 9.9959E-06

3.2 1.24712E-05

3.3 1.55207E-05

3.4 1.92676E-05

3.5 2.38593E-053.6 2.94715E-05

3.7 3.6313E-05

3.8 4.46308E-05

3.9 5.4717E-05

4 6.69151E-05

4.1 8.16282E-05

4.2 9.93277E-05

4.3 0.000120563

4.4 0.000145973

4.5 0.000176298

4.6 0.00021239

4.7 0.000255232

4.8 0.000305951

4.9 0.000365832

5 0.000436341

5.1 0.000519141

5.2 0.00061611

5.3 0.000729365

5.4 0.000861284

5.5 0.001014524

5.6 0.0011920445.7 0.001397129

5.8 0.00163341

5.9 0.001904881

6 0.002215924

6.1 0.00257132

6.2 0.002976266

6.3 0.003436383

6.4 0.003957726

6.5 0.004546781

6.6 0.005210467

6.7 0.0059561226.8 0.006791485

6.9 0.007724674

7 0.00876415

7.1 0.009918677

7.2 0.011197265

7.3 0.01260911

7.4 0.014163519

7.5 0.015869826


266/331

7.6 0.017737296

7.7 0.019775021

7.8 0.021991798

7.9 0.024396009

8 0.026995483

8.1 0.029797353

8.2 0.0328079078.3 0.036032437

8.4 0.039475079

8.5 0.043138659

8.6 0.047024539

8.7 0.051132462

8.8 0.055460417

8.9 0.0600045

9 0.064758798

9.1 0.069715283

9.2 0.074863733

9.3 0.080191664

9.4 0.085684296

9.5 0.091324543

9.6 0.097093027

9.7 0.102968134

9.8 0.108926089

9.9 0.11494107

10 0.120985362

10.1 0.127029528

10.2 0.133042625

10.3 0.13899244310.4 0.144845776

10.5 0.150568716

10.6 0.156126967

10.7 0.16148618

10.8 0.166612301

10.9 0.171471928

11 0.176032663

11.1 0.180263481

11.2 0.18413507

11.3 0.187620173

11.4 0.19069390811.5 0.193334058

11.6 0.195521347

11.7 0.197239665

11.8 0.198476274

11.9 0.199221957

12 0.19947114

12.1 0.199221957

12.2 0.198476274


267/331

12.3 0.197239665

12.4 0.195521347

12.5 0.193334058

12.6 0.190693908

12.7 0.187620173

12.8 0.18413507

12.9 0.18026348113 0.176032663

13.1 0.171471928

13.2 0.166612301

13.3 0.16148618

13.4 0.156126967

13.5 0.150568716

13.6 0.144845776

13.7 0.138992443

13.8 0.133042625

13.9 0.127029528

14 0.120985362

14.1 0.11494107

14.2 0.108926089

14.3 0.102968134

14.4 0.097093027

14.5 0.091324543

14.6 0.085684296

14.7 0.080191664

14.8 0.074863733

14.9 0.069715283

15 0.06475879815.1 0.0600045

15.2 0.055460417

15.3 0.051132462

15.4 0.047024539

15.5 0.043138659

15.6 0.039475079

15.7 0.036032437

15.8 0.032807907

15.9 0.029797353

16 0.026995483

16.1 0.02439600916.2 0.021991798

16.3 0.019775021

16.4 0.017737296

16.5 0.015869826

16.6 0.014163519

16.7 0.01260911

16.8 0.011197265

16.9 0.009918677


268/331

17 0.00876415

17.1 0.007724674

17.2 0.006791485

17.3 0.005956122

17.4 0.005210467

17.5 0.004546781

17.6 0.00395772617.7 0.003436383

17.8 0.002976266

17.9 0.00257132

18 0.002215924

18.1 0.001904881

18.2 0.00163341

18.3 0.001397129

18.4 0.001192044

18.5 0.001014524

18.6 0.000861284

18.7 0.000729365

18.8 0.00061611

18.9 0.000519141

19 0.000436341

19.1 0.000365832

19.2 0.000305951

19.3 0.000255232

19.4 0.00021239

19.5 0.000176298

19.6 0.000145973

19.7 0.00012056319.8 9.93277E-05

19.9 8.16282E-05

20 6.69151E-05

Total is not 1 because not Probability 9.999715622


269/331

ST(C2,C6,C7,1)

Area for>=10 and

=$C$2,E17=10 and


270/331


271/331

0.120985362

0.127029528

0.133042625

0.1389924430.144845776

0.150568716

0.156126967

0.16148618

0.166612301

0.171471928

0.176032663

0.180263481

0.18413507

0.187620173

0.1906939080.193334058

0.195521347

0.197239665

0.198476274

0.199221957

0.19947114

0.199221957

0.198476274


272/331

0.197239665

0.195521347

0.193334058

0.190693908

0.187620173

0.18413507

0.1802634810.176032663

0.171471928

0.166612301

0.16148618

0.156126967

0.150568716

0.144845776

0.138992443

0.133042625

0.127029528

0.120985362


273/331


274/331

If the professor grades with a bell curve and assigns a grade of A for the top 5.00% of

the scores, what score would you need to get to earn an A if the mean (from past

data) was 79 and the standard deviation (from past data) was 6?

What is x? Scores

Mean 79SD 6

Probability 5.00%

X = Score Needed =NORMINV(1-B6,B4,B5)

or z = (x-mu)/sigma=>

z x = z*sigma+mu

X = Score Needed =B11*B5+B4

From past population data that has a normal shaped distribution, if the employees on

average produced 1000 boomerangs per day with a standard deviation of 50 how

many boomerangs would have to be produced for the day's production level to be

among the slowest 10.00% of days?

What is x? # units produced

Mean 1000

SD 50

Probability 0.1

X = Score Needed =NORMINV(B19,B17,B18)


z x = z*sigma+mu

X = Score Needed =B24*B18+B17


275/331


276/331

Data For Questions

796

5%

Data For Questions

1000

50

10%


277/331

If the professor grades with a bell curve and assigns a grade of A for the top 5.00% of

the scores, what score would you need to get to earn an A if the mean (from past

data) was 79 and the standard deviation (from past data) was 6?

What is x? Scores

Mean 79SD 6

Probability 5.00%

X = Score Needed 88.86912176 =NORMINV(1-B6,B4,B5)


z 1.644853627 x = z*sigma+mu

X = Score Needed 88.86912176 =B11*B5+B4

From past population data that has a normal shaped distribution, if the employees on

average produced 1000 boomerangs per day with a standard deviation of 50 how

many boomerangs would have to be produced for the day's production level to be

among the slowest 10.00% of days?

What is x? # units produced

Mean 1000

SD 50

Probability 0.1

X = Score Needed 935.9224217 =NORMINV(B19,B17,B18)


z -1.281551566 x = z*sigma+mu

X = Score Needed 935.9224217 =B24*B18+B17


278/331


279/331

Data For Questions

796

5%

Data For Questions

1000

50

10%


280/331

Exponential Probability Distribution

Continuous Random Variable

X > = 0

Mean = Standard Deviation

Excel function: EXPONDIST

EXPONDIST(x,1/mu, (0 = exact, 1 = cumulative)) or cumulative function = 1 - e^(-x/

According to a recent study, business people are interrupted 5.5 times per hour.

Assume that the distribution follows an Exponetial Distribution

Mean for Poisson Distribution = # interruptions = 5.5 per 1 hour

x # interruptions 5.5 per 1 hour

60 minutes

Mean for Exponetial Distribution = x = Time between interruptions =

0.181818181818182 hours

x x = Time between interruptions 0.18182 hours

10.9091 minutes

P(get interrupted in the next 10 minutes)

x1 x2

0 10 minutes

P(x15) 0.25284 =EXP(1)^(-D23/$C$14)

x (min) f(x) P(x15) = .

0 0.091666667 0.09167

0.1 0.090830228 0.09083

0.2 0.090001422 0.09

0.3 0.089180179 0.08918

0.4 0.08836643 0.08837

0.5 0.087560105 0.08756

0.6 0.086761139 0.08676

0.7 0.085969462 0.08597

0.8 0.08518501 0.08519

0.9 0.084407715 0.084411 0.083637513 0.08364

1.1 0.082874339 0.08287

1.2 0.082118129 0.08212

1.3 0.081368819 0.08137

1.4 0.080626346 0.08063

1.5 0.079890649 0.07989

1.6 0.079161664 0.07916

1.7 0.078439331 0.07844

0

0.05

0.1

0

2.3

4.6

According t

per ho


281/331

1.8 0.07772359 0.07772

1.9 0.077014379 0.07701

2 0.076311639 0.07631

2.1 0.075615313 0.07562

2.2 0.074925339 0.07493

2.3 0.074241662 0.07424

2.4 0.073564223 0.073562.5 0.072892966 0.07289

2.6 0.072227833 0.07223

2.7 0.07156877 0.07157

2.8 0.070915721 0.07092

2.9 0.07026863 0.07027

3 0.069627445 0.06963

3.1 0.068992109 0.06899

3.2 0.068362572 0.06836

3.3 0.067738778 0.06774

3.4 0.067120677 0.06712

3.5 0.066508215 0.06651

3.6 0.065901342 0.0659

3.7 0.065300007 0.0653

3.8 0.064704159 0.0647

3.9 0.064113747 0.06411

4 0.063528724 0.06353

4.1 0.062949038 0.06295

4.2 0.062374642 0.06237

4.3 0.061805487 0.06181

4.4 0.061241525 0.06124

4.5 0.06068271 0.060684.6 0.060128993 0.06013

4.7 0.059580329 0.05958

4.8 0.059036672 0.05904

4.9 0.058497975 0.0585

5 0.057964194 0.05796

5.1 0.057435283 0.05744

5.2 0.056911199 0.05691

5.3 0.056391897 0.05639

5.4 0.055877333 0.05588

5.5 0.055367465 0.05537

5.6 0.054862249 0.054865.7 0.054361643 0.05436

5.8 0.053865605 0.05387

5.9 0.053374093 0.05337

6 0.052887066 0.05289

6.1 0.052404483 0.0524

6.2 0.051926304 0.05193

6.3 0.051452487 0.05145

6.4 0.050982995 0.05098


282/331

6.5 0.050517786 0.05052

6.6 0.050056822 0.05006

6.7 0.049600065 0.0496

6.8 0.049147475 0.04915

6.9 0.048699015 0.0487

7 0.048254647 0.04825

7.1 0.047814334 0.047817.2 0.047378039 0.04738

7.3 0.046945725 0.04695

7.4 0.046517355 0.04652

7.5 0.046092895 0.04609

7.6 0.045672307 0.04567

7.7 0.045255557 0.04526

7.8 0.04484261 0.04484

7.9 0.044433431 0.04443

8 0.044027986 0.04403

8.1 0.04362624 0.04363

8.2 0.04322816 0.04323

8.3 0.042833713 0.04283

8.4 0.042442865 0.04244

8.5 0.042055583 0.04206

8.6 0.041671835 0.04167

8.7 0.041291588 0.04129

8.8 0.040914812 0.04091

8.9 0.040541473 0.04054

9 0.040171541 0.04017

9.1 0.039804984 0.0398

9.2 0.039441773 0.039449.3 0.039081875 0.03908

9.4 0.038725262 0.03873

9.5 0.038371902 0.03837

9.6 0.038021767 0.03802

9.7 0.037674827 0.03767

9.8 0.037331052 0.03733

9.9 0.036990414 0.03699

10 0.036652885 0.03665

10.1 0.036318435

10.2 0.035987038

10.3 0.03565866410.4 0.035333286

10.5 0.035010878

10.6 0.034691411

10.7 0.03437486

10.8 0.034061197

10.9 0.033750396

11 0.033442431

11.1 0.033137276


283/331

11.2 0.032834906

11.3 0.032535294

11.4 0.032238417

11.5 0.031944248

11.6 0.031652764

11.7 0.031363939

11.8 0.0310777511.9 0.030794173

12 0.030513183

12.1 0.030234757

12.2 0.029958871

12.3 0.029685503

12.4 0.029414629

12.5 0.029146227

12.6 0.028880274

12.7 0.028616748

12.8 0.028355626

12.9 0.028096888

13 0.02784051

13.1 0.027586471

13.2 0.027334751

13.3 0.027085327

13.4 0.026838179

13.5 0.026593287

13.6 0.026350629

13.7 0.026110185

13.8 0.025871935

13.9 0.0256358614 0.025401938

14.1 0.025170151

14.2 0.024940479

14.3 0.024712902

14.4 0.024487403

14.5 0.02426396

14.6 0.024042557

14.7 0.023823174

14.8 0.023605793

14.9 0.023390395

15 0.02317696315.1 0.022965478 0.02297

15.2 0.022755923 0.02276

15.3 0.02254828 0.02255

15.4 0.022342532 0.02234

15.5 0.022138662 0.02214

15.6 0.021936651 0.02194

15.7 0.021736484 0.02174

15.8 0.021538143 0.02154


284/331

15.9 0.021341613 0.02134

16 0.021146875 0.02115

16.1 0.020953914 0.02095

16.2 0.020762715 0.02076

16.3 0.020573259 0.02057

16.4 0.020385533 0.02039

16.5 0.020199519 0.020216.6 0.020015203 0.02002

16.7 0.019832569 0.01983

16.8 0.019651601 0.01965

16.9 0.019472284 0.01947

17 0.019294604 0.01929

17.1 0.019118545 0.01912

17.2 0.018944093 0.01894

17.3 0.018771232 0.01877

17.4 0.018599948 0.0186

17.5 0.018430228 0.01843

17.6 0.018262056 0.01826

17.7 0.018095419 0.0181

17.8 0.017930302 0.01793

17.9 0.017766692 0.01777

18 0.017604575 0.0176

18.1 0.017443937 0.01744

18.2 0.017284765 0.01728

18.3 0.017127045 0.01713

18.4 0.016970765 0.01697

18.5 0.01681591 0.01682

18.6 0.016662469 0.0166618.7 0.016510427 0.01651

18.8 0.016359773 0.01636

18.9 0.016210494 0.01621

19 0.016062577 0.01606

19.1 0.015916009 0.01592

19.2 0.015770779 0.01577

19.3 0.015626874 0.01563

19.4 0.015484282 0.01548

19.5 0.015342992 0.01534

19.6 0.01520299 0.0152

19.7 0.015064266 0.0150619.8 0.014926808 0.01493

19.9 0.014790604 0.01479

20 0.014655643 0.01466

20.1 0.014521914 0.01452

20.2 0.014389405 0.01439

20.3 0.014258104 0.01426

20.4 0.014128002 0.01413

20.5 0.013999087 0.014


285/331

20.6 0.013871349 0.01387

20.7 0.013744776 0.01374

20.8 0.013619358 0.01362

20.9 0.013495084 0.0135

21 0.013371944 0.01337

21.1 0.013249928 0.01325

21.2 0.013129026 0.0131321.3 0.013009226 0.01301

21.4 0.01289052 0.01289

21.5 0.012772897 0.01277

21.6 0.012656347 0.01266

21.7 0.01254086 0.01254

21.8 0.012426428 0.01243

21.9 0.012313039 0.01231

22 0.012200686 0.0122

22.1 0.012089357 0.01209

22.2 0.011979044 0.01198

22.3 0.011869738 0.01187

22.4 0.011761429 0.01176

22.5 0.011654109 0.01165

22.6 0.011547768 0.01155

22.7 0.011442397 0.01144

22.8 0.011337987 0.01134

22.9 0.011234531 0.01123

23 0.011132018 0.01113

23.1 0.011030441 0.01103

23.2 0.010929791 0.01093

23.3 0.010830059 0.0108323.4 0.010731237 0.01073

23.5 0.010633317 0.01063

23.6 0.01053629 0.01054

23.7 0.010440149 0.01044

23.8 0.010344884 0.01034

23.9 0.01025049 0.01025

24 0.010156956 0.01016

24.1 0.010064276 0.01006

24.2 0.009972442 0.00997

24.3 0.009881446 0.00988

24.4 0.009791279 0.0097924.5 0.009701936 0.0097

24.6 0.009613408 0.00961

24.7 0.009525688 0.00953

24.8 0.009438768 0.00944

24.9 0.009352641 0.00935

25 0.009267301 0.00927

25.1 0.009182739 0.00918

25.2 0.009098948 0.0091


286/331

25.3 0.009015922 0.00902

25.4 0.008933654 0.00893

25.5 0.008852136 0.00885

25.6 0.008771362 0.00877

25.7 0.008691326 0.00869

25.8 0.008612019 0.00861

25.9 0.008533436 0.0085326 0.008455571 0.00846

26.1 0.008378415 0.00838

26.2 0.008301964 0.0083

26.3 0.008226211 0.00823

26.4 0.008151148 0.00815

26.5 0.008076771 0.00808

26.6 0.008003072 0.008

26.7 0.007930046 0.00793

26.8 0.007857686 0.00786

26.9 0.007785986 0.00779

27 0.007714941 0.00771

27.1 0.007644544 0.00764

27.2 0.007574789 0.00757

27.3 0.007505671 0.00751

27.4 0.007437183 0.00744

27.5 0.00736932 0.00737

27.6 0.007302077 0.0073

27.7 0.007235447 0.00724

27.8 0.007169425 0.00717

27.9 0.007104006 0.0071

28 0.007039183 0.0070428.1 0.006974952 0.00697

28.2 0.006911307 0.00691

28.3 0.006848243 0.00685

28.4 0.006785754 0.00679

28.5 0.006723836 0.00672

28.6 0.006662482 0.00666

28.7 0.006601689 0.0066

28.8 0.00654145 0.00654

28.9 0.00648176 0.00648

29 0.006422616 0.00642

29.1 0.006364011 0.0063629.2 0.006305941 0.00631

29.3 0.0062484 0.00625

29.4 0.006191385 0.00619

29.5 0.00613489 0.00613

29.6 0.00607891 0.00608

29.7 0.006023442 0.00602

29.8 0.005968479 0.00597

29.9 0.005914018 0.00591


287/331

30 0.005860054 0.00586

30.1 0.005806582 0.00581

30.2 0.005753598 0.00575

30.3 0.005701098 0.0057

30.4 0.005649077 0.00565

30.5 0.00559753 0.0056

30.6 0.005546454 0.0055530.7 0.005495844 0.0055

30.8 0.005445695 0.00545

30.9 0.005396005 0.0054

31 0.005346767 0.00535

31.1 0.005297979 0.0053

31.2 0.005249636 0.00525

31.3 0.005201735 0.0052

31.4 0.00515427 0.00515

31.5 0.005107238 0.00511

31.6 0.005060636 0.00506

31.7 0.005014459 0.00501

31.8 0.004968703 0.00497

31.9 0.004923365 0.00492

32 0.00487844 0.00488

32.1 0.004833925 0.00483

32.2 0.004789817 0.00479

32.3 0.004746111 0.00475

32.4 0.004702803 0.0047

32.5 0.004659891 0.00466

32.6 0.004617371 0.00462

32.7 0.004575238 0.0045832.8 0.00453349 0.00453

32.9 0.004492123 0.00449

33 0.004451134 0.00445

33.1 0.004410518 0.00441

33.2 0.004370273 0.00437

33.3 0.004330395 0.00433

33.4 0.004290881 0.00429

33.5 0.004251728 0.00425

33.6 0.004212932 0.00421

33.7 0.00417449 0.00417

33.8 0.004136398 0.0041433.9 0.004098655 0.0041

34 0.004061255 0.00406

34.1 0.004024197 0.00402

34.2 0.003987477 0.00399

34.3 0.003951093 0.00395

34.4 0.00391504 0.00392

34.5 0.003879316 0.00388

34.6 0.003843918 0.00384


288/331

34.7 0.003808843 0.00381

34.8 0.003774088 0.00377

34.9 0.00373965 0.00374

35 0.003705527 0.00371

35.1 0.003671715 0.00367

35.2 0.003638211 0.00364

35.3 0.003605013 0.0036135.4 0.003572118 0.00357

35.5 0.003539524 0.00354

35.6 0.003507226 0.00351

35.7 0.003475224 0.00348

35.8 0.003443513 0.00344

35.9 0.003412092 0.00341

36 0.003380957 0.00338

36.1 0.003350107 0.00335

36.2 0.003319538 0.00332

36.3 0.003289247 0.00329

36.4 0.003259234 0.00326

36.5 0.003229494 0.00323

36.6 0.003200026 0.0032

36.7 0.003170826 0.00317

36.8 0.003141893 0.00314

36.9 0.003113224 0.00311

37 0.003084816 0.00308

37.1 0.003056668 0.00306

37.2 0.003028777 0.00303

37.3 0.00300114 0.003

37.4 0.002973755 0.0029737.5 0.00294662 0.00295

37.6 0.002919733 0.00292

37.7 0.002893091 0.00289

37.8 0.002866692 0.00287

37.9 0.002840534 0.00284

38 0.002814615 0.00281

38.1 0.002788932 0.00279

38.2 0.002763484 0.00276

38.3 0.002738268 0.00274

38.4 0.002713282 0.00271

38.5 0.002688523 0.0026938.6 0.002663991 0.00266

38.7 0.002639683 0.00264

38.8 0.002615596 0.00262

38.9 0.00259173 0.00259

39 0.002568081 0.00257

39.1 0.002544648 0.00254

39.2 0.002521428 0.00252

39.3 0.002498421 0.0025


289/331

39.4 0.002475623 0.00248

39.5 0.002453034 0.00245

39.6 0.00243065 0.00243

39.7 0.002408471 0.00241

39.8 0.002386494 0.00239

39.9 0.002364718 0.00236

40 0.002343141 0.0023440.1 0.00232176 0.00232

40.2 0.002300574 0.0023

40.3 0.002279582 0.00228

40.4 0.002258781 0.00226

40.5 0.002238171 0.00224

40.6 0.002217748 0.00222

40.7 0.002197511 0.0022

40.8 0.002177459 0.00218

40.9 0.002157591 0.00216

41 0.002137903 0.00214

41.1 0.002118395 0.00212

41.2 0.002099065 0.0021

41.3 0.002079912 0.00208

41.4 0.002060933 0.00206

41.5 0.002042127 0.00204

41.6 0.002023494 0.00202

41.7 0.00200503 0.00201

41.8 0.001986734 0.00199

41.9 0.001968606 0.00197

42 0.001950643 0.00195

42.1 0.001932843 0.0019342.2 0.001915207 0.00192

42.3 0.001897731 0.0019

42.4 0.001880414 0.00188

42.5 0.001863256 0.00186

42.6 0.001846254 0.00185

42.7 0.001829407 0.00183

42.8 0.001812715 0.00181

42.9 0.001796174 0.0018

43 0.001779784 0.00178

43.1 0.001763544 0.00176

43.2 0.001747452 0.0017543.3 0.001731507 0.00173

43.4 0.001715707 0.00172

43.5 0.001700052 0.0017

43.6 0.001684539 0.00168

43.7 0.001669168 0.00167

43.8 0.001653938 0.00165

43.9 0.001638846 0.00164

44 0.001623892 0.00162


290/331

44.1 0.001609074 0.00161

44.2 0.001594391 0.00159

44.3 0.001579843 0.00158

44.4 0.001565427 0.00157

44.5 0.001551143 0.00155

44.6 0.001536989 0.00154

44.7 0.001522965 0.0015244.8 0.001509068 0.00151

44.9 0.001495298 0.0015

45 0.001481654 0.00148

45.1 0.001468134 0.00147

45.2 0.001454738 0.00145

45.3 0.001441463 0.00144

45.4 0.00142831 0.00143

45.5 0.001415277 0.00142

45.6 0.001402363 0.0014

45.7 0.001389567 0.00139

45.8 0.001376887 0.00138

45.9 0.001364324 0.00136

46 0.001351874 0.00135

46.1 0.001339539 0.00134

46.2 0.001327316 0.00133

46.3 0.001315204 0.00132

46.4 0.001303204 0.0013

46.5 0.001291312 0.00129

46.6 0.001279529 0.00128

46.7 0.001267854 0.00127

46.8 0.001256285 0.0012646.9 0.001244821 0.00124

47 0.001233463 0.00123

47.1 0.001222208 0.00122

47.2 0.001211055 0.00121

47.3 0.001200005 0.0012

47.4 0.001189055 0.00119

47.5 0.001178205 0.00118

47.6 0.001167454 0.00117

47.7 0.001156801 0.00116

47.8 0.001146246 0.00115

47.9 0.001135787 0.0011448 0.001125423 0.00113

48.1 0.001115154 0.00112

48.2 0.001104978 0.0011

48.3 0.001094895 0.00109

48.4 0.001084905 0.00108

48.5 0.001075005 0.00108

48.6 0.001065196 0.00107

48.7 0.001055476 0.00106


291/331

48.8 0.001045845 0.00105

48.9 0.001036302 0.00104

49 0.001026846 0.00103

49.1 0.001017476 0.00102

49.2 0.001008192 0.00101

49.3 0.000998993 0.001

49.4 0.000989877 0.0009949.5 0.000980845 0.00098

49.6 0.000971895 0.00097

49.7 0.000963026 0.00096

49.8 0.000954239 0.00095

49.9 0.000945532 0.00095

50 0.000936904 0.00094


292/331

mu)

1 - e^(-x/mu)

6.9

9.2

11

.5

13

.8

16

.1

18

.4

20

.7

23

25

.3

27

.6

29

.9

32

.2

34

.5

36

.8

39

.1

41

.4

43

.7

46

48

.3

x = Time between interruptions

o a recent study, business people are interrupted 5.5 times

ur. Assume that the distribution follows an Exponetial

Distribution

f(x) P(x15) = 25.28%


293/331

Relationship between Poisson and Exponential

Poisson is # of occurrences during per Interval

Exponential is length between occurrences

If occurrences follow a Poisson Distr., the length between occurrences must follow an

Exponential Distribution



60 minutes

Mean for Exponetial Distribution = Time between interruptions = hours

x Time between interruptions hours

minutes

P(no interruptions during 15 minute period 0 to 15)

x1 x2

0 15 minutes

P(X>15) Exponential, x = time between occurrences

x = 0 # of occurrences

Time =

Mean = # occurrences per 15

minutes

P(x


294/331

Poisson Probability Distribution can be used to esti

over a specified interval of ti

Discrete Random Vari

Properties of a Poisson Ex

The probability of an occurrence is the same for a

The occurrence or nonoccurrence in any interval is

nonoccurrence in any othe

No upper limit for X: 0,1,2,3 , but as x increases

decreases and gets quit

Mean = Var

Excel function: POISS

POISSON(x,mean,cumulative (0 = exa

=1-EXPONDIST(D12,1/C7,1)

=POISSON(C15,C17,0)


295/331

imate the number of occurrences

me or space

Exponential Probability Distribution can be used to estimate the leng

between occurrences (time or space)

iable Continuous Random Variable

X > = 0


independent of the occurrence or

er interval Excel function: EXPONDIST

EXPONDIST(x,1/mu, (0 = exact, 1 = cumulative))

act, 1 = cumulative))


296/331

th of the interval


297/331

Relationship between Poisson and Exponential

Poisson is # of occurrences during per Interval

Exponential is length between occurrences

If occurrences follow a Poisson Distr., the length between occurrences must follow an

Exponential Distribution



60 minutes

Mean for Exponetial Distribution = Time between interruptions = 0.181818181818182

hours

x Time between interruptions 0.18181818 hours

10.9090909 minutes

P(no interruptions during 15 minute period 0 to 15)

x1 x2

0 15 minutes

P(X>15) 0.2528396 Exponential, x = time between occurrences

x = 0 # of occurrences

Time = 0.25

Mean = # occurrences per 15

minutes 1.375

P(x


298/331

Poisson Probability Distribution can be used to esti

over a specified interval of ti

Discrete Random Vari

Properties of a Poisson Ex

The probability of an occurrence is the same for a

The occurrence or nonoccurrence in any interval is

nonoccurrence in any othe

No upper limit for X: 0,1,2,3 , but as x increases

decreases and gets quit

Mean = Var

Excel function: POISS

POISSON(x,mean,cumulative (0 = exa

=1-EXPONDIST(D12,1/C7,1)

=POISSON(C15,C17,0)


299/331

imate the number of occurrences

me or space

Exponential Probability Distribution can be used to estimate the leng

between occurrences (time or space)

iable Continuous Random Variable

X > = 0


independent of the occurrence or

er interval Excel function: EXPONDIST

EXPONDIST(x,1/mu, (0 = exact, 1 = cumulative))

act, 1 = cumulative))


300/331

th of the interval


301/331

For a particular Disney Ride, the mean time to

wait in line is 22 minutes (Distribution follows an

Exponential Distribution pattern.

mu 22 time to stand in line

x 15

P(x=25) =1-EXPONDIST(B6,1/B2,1)

P(15


302/331

3.1 0.03948

3.2 0.039301

3.3 0.039123

3.4 0.038946

3.5 0.038769

3.6 0.038593

3.7 0.0384183.8 0.038244

3.9 0.038071

4 0.037898

4.1 0.037726

4.2 0.037555

4.3 0.037385

4.4 0.037215

4.5 0.037046

4.6 0.036878

4.7 0.036711

4.8 0.036545

4.9 0.036379

5 0.036214

5.1 0.03605

5.2 0.035886

5.3 0.035723

5.4 0.035561

5.5 0.0354

5.6 0.035239

5.7 0.03508

5.8 0.0349215.9 0.034762

6 0.034605

6.1 0.034448

6.2 0.034291

6.3 0.034136

6.4 0.033981

6.5 0.033827

6.6 0.033674

6.7 0.033521

6.8 0.033369

6.9 0.0332177 0.033067

7.1 0.032917

7.2 0.032768

7.3 0.032619

7.4 0.032471

7.5 0.032324

7.6 0.032177

7.7 0.032031


303/331

7.8 0.031886

7.9 0.031741

8 0.031597

8.1 0.031454

8.2 0.031312

8.3 0.03117

8.4 0.0310288.5 0.030887

8.6 0.030747

8.7 0.030608

8.8 0.030469

8.9 0.030331

9 0.030193

9.1 0.030056

9.2 0.02992

9.3 0.029784

9.4 0.029649

9.5 0.029515

9.6 0.029381

9.7 0.029248

9.8 0.029115

9.9 0.028983

10 0.028852

10.1 0.028721

10.2 0.028591

10.3 0.028461

10.4 0.028332

10.5 0.02820310.6 0.028075

10.7 0.027948

10.8 0.027821

10.9 0.027695

11 0.02757

11.1 0.027445

11.2 0.02732

11.3 0.027196

11.4 0.027073

11.5 0.02695

11.6 0.02682811.7 0.026706

11.8 0.026585

11.9 0.026464

12 0.026344

12.1 0.026225

12.2 0.026106

12.3 0.025988

12.4 0.02587


304/331

12.5 0.025752

12.6 0.025636

12.7 0.025519

12.8 0.025404

12.9 0.025288

13 0.025174

13.1 0.0250613.2 0.024946

13.3 0.024833

13.4 0.02472

13.5 0.024608

13.6 0.024497

13.7 0.024385

13.8 0.024275

13.9 0.024165

14 0.024055

14.1 0.023946

14.2 0.023837

14.3 0.023729

14.4 0.023622

14.5 0.023515

14.6 0.023408

14.7 0.023302

14.8 0.023196

14.9 0.023091

15 0.022986

15.1 0.022882

15.2 0.02277815.3 0.022675

15.4 0.022572

15.5 0.02247

15.6 0.022368

15.7 0.022266

15.8 0.022165

15.9 0.022065

16 0.021965

16.1 0.021865

16.2 0.021766

16.3 0.02166716.4 0.021569

16.5 0.021471

16.6 0.021374

16.7 0.021277

16.8 0.02118

16.9 0.021084

17 0.020989

17.1 0.020894


305/331

17.2 0.020799

17.3 0.020704

17.4 0.020611

17.5 0.020517

17.6 0.020424

17.7 0.020331

17.8 0.02023917.9 0.020147

18 0.020056

18.1 0.019965

18.2 0.019875

18.3 0.019784

18.4 0.019695

18.5 0.019605

18.6 0.019516

18.7 0.019428

18.8 0.01934

18.9 0.019252

19 0.019165

19.1 0.019078

19.2 0.018991

19.3 0.018905

19.4 0.01882

19.5 0.018734

19.6 0.018649

19.7 0.018565

19.8 0.01848

19.9 0.01839720 0.018313

20.1 0.01823

20.2 0.018147

20.3 0.018065

20.4 0.017983

20.5 0.017902

20.6 0.01782

20.7 0.01774

20.8 0.017659

20.9 0.017579

21 0.01749921.1 0.01742

21.2 0.017341

21.3 0.017262

21.4 0.017184

21.5 0.017106

21.6 0.017029

21.7 0.016951

21.8 0.016875


306/331

21.9 0.016798

22 0.016722

22.1 0.016646

22.2 0.01657

22.3 0.016495

22.4 0.016421

22.5 0.01634622.6 0.016272

22.7 0.016198

22.8 0.016125

22.9 0.016052

23 0.015979

23.1 0.015906

23.2 0.015834

23.3 0.015762

23.4 0.015691

23.5 0.01562

23.6 0.015549

23.7 0.015478

23.8 0.015408

23.9 0.015338

24 0.015269

24.1 0.015199

24.2 0.015131

24.3 0.015062

24.4 0.014994

24.5 0.014926

24.6 0.01485824.7 0.014791

24.8 0.014723

24.9 0.014657

25 0.01459

25.1 0.014524

25.2 0.014458

25.3 0.014393

25.4 0.014327

25.5 0.014262

25.6 0.014198

25.7 0.01413325.8 0.014069

25.9 0.014005

26 0.013942

26.1 0.013879

26.2 0.013816

26.3 0.013753

26.4 0.013691

26.5 0.013629


307/331

26.6 0.013567

26.7 0.013505

26.8 0.013444

26.9 0.013383

27 0.013322

27.1 0.013262

27.2 0.01320227.3 0.013142

27.4 0.013082

27.5 0.013023

27.6 0.012964

27.7 0.012905

27.8 0.012847

27.9 0.012788

28 0.01273

28.1 0.012673

28.2 0.012615

28.3 0.012558

28.4 0.012501

28.5 0.012444

28.6 0.012388

28.7 0.012332

28.8 0.012276

28.9 0.01222

29 0.012165

29.1 0.012109

29.2 0.012055

29.3 0.01229.4 0.011945

29.5 0.011891

29.6 0.011837

29.7 0.011784

29.8 0.01173

29.9 0.011677

30 0.011624

30.1 0.011571

30.2 0.011519

30.3 0.011467

30.4 0.01141530.5 0.011363

30.6 0.011311

30.7 0.01126

30.8 0.011209

30.9 0.011158

31 0.011108

31.1 0.011057

31.2 0.011007


308/331

31.3 0.010957

31.4 0.010907

31.5 0.010858

31.6 0.010809

31.7 0.01076

31.8 0.010711

31.9 0.01066232 0.010614

32.1 0.010566

32.2 0.010518

32.3 0.01047

32.4 0.010423

32.5 0.010375

32.6 0.010328

32.7 0.010282

32.8 0.010235

32.9 0.010188

33 0.010142

33.1 0.010096

33.2 0.01005

33.3 0.010005

33.4 0.00996

33.5 0.009914

33.6 0.009869

33.7 0.009825

33.8 0.00978

33.9 0.009736

34 0.00969234.1 0.009648

34.2 0.009604

34.3 0.00956

34.4 0.009517

34.5 0.009474

34.6 0.009431

34.7 0.009388

34.8 0.009345

34.9 0.009303

35 0.009261

35.1 0.00921935.2 0.009177

35.3 0.009135

35.4 0.009094

35.5 0.009053

35.6 0.009012

35.7 0.008971

35.8 0.00893

35.9 0.00889


309/331

36 0.008849

36.1 0.008809

36.2 0.008769

36.3 0.00873

36.4 0.00869

36.5 0.008651

36.6 0.00861136.7 0.008572

36.8 0.008533

36.9 0.008495

37 0.008456

37.1 0.008418

37.2 0.00838

37.3 0.008342

37.4 0.008304

37.5 0.008266

37.6 0.008229

37.7 0.008191

37.8 0.008154

37.9 0.008117

38 0.00808

38.1 0.008044

38.2 0.008007

38.3 0.007971

38.4 0.007935

38.5 0.007899

38.6 0.007863

38.7 0.00782738.8 0.007792

38.9 0.007756

39 0.007721

39.1 0.007686

39.2 0.007651

39.3 0.007617

39.4 0.007582

39.5 0.007548

39.6 0.007514

39.7 0.00748

39.8 0.00744639.9 0.007412

40 0.007378

40.1 0.007345

40.2 0.007311

40.3 0.007278

40.4 0.007245

40.5 0.007212

40.6 0.00718


310/331

40.7 0.007147

40.8 0.007115

40.9 0.007082

41 0.00705

41.1 0.007018

41.2 0.006987

41.3 0.00695541.4 0.006923

41.5 0.006892

41.6 0.006861

41.7 0.00683

41.8 0.006799

41.9 0.006768

42 0.006737

42.1 0.006706

42.2 0.006676

42.3 0.006646

42.4 0.006616

42.5 0.006586

42.6 0.006556

42.7 0.006526

42.8 0.006496

42.9 0.006467

43 0.006438

43.1 0.006408

43.2 0.006379

43.3 0.00635

43.4 0.00632243.5 0.006293

43.6 0.006264

43.7 0.006236

43.8 0.006208

43.9 0.00618

44 0.006152

44.1 0.006124

44.2 0.006096

44.3 0.006068

44.4 0.006041

44.5 0.00601344.6 0.005986

44.7 0.005959

44.8 0.005932

44.9 0.005905

45 0.005878

45.1 0.005852

45.2 0.005825

45.3 0.005799


311/331

45.4 0.005772

45.5 0.005746

45.6 0.00572

45.7 0.005694

45.8 0.005668

45.9 0.005643

46 0.00561746.1 0.005592

46.2 0.005566

46.3 0.005541

46.4 0.005516

46.5 0.005491

46.6 0.005466

46.7 0.005441

46.8 0.005416

46.9 0.005392

47 0.005367

47.1 0.005343

47.2 0.005319

47.3 0.005295

47.4 0.005271

47.5 0.005247

47.6 0.005223

47.7 0.005199

47.8 0.005176

47.9 0.005152

48 0.005129

48.1 0.00510648.2 0.005083

48.3 0.005059

48.4 0.005037

48.5 0.005014

48.6 0.004991

48.7 0.004968

48.8 0.004946

48.9 0.004923

49 0.004901

49.1 0.004879

49.2 0.00485749.3 0.004835

49.4 0.004813

49.5 0.004791

49.6 0.004769

49.7 0.004748

49.8 0.004726

49.9 0.004705

50 0.004683


312/331

50.1 0.004662

50.2 0.004641

50.3 0.00462

50.4 0.004599

50.5 0.004578

50.6 0.004557

50.7 0.00453750.8 0.004516

50.9 0.004495

51 0.004475

51.1 0.004455

51.2 0.004435

51.3 0.004415

51.4 0.004394

51.5 0.004375

51.6 0.004355

51.7 0.004335

51.8 0.004315

51.9 0.004296

52 0.004276

52.1 0.004257

52.2 0.004238

52.3 0.004218

52.4 0.004199

52.5 0.00418

52.6 0.004161

52.7 0.004142

52.8 0.00412452.9 0.004105

53 0.004086

53.1 0.004068

53.2 0.004049

53.3 0.004031

53.4 0.004013

53.5 0.003994

53.6 0.003976

53.7 0.003958

53.8 0.00394

53.9 0.00392254 0.003905

54.1 0.003887

54.2 0.003869

54.3 0.003852

54.4 0.003834

54.5 0.003817

54.6 0.0038

54.7 0.003782


313/331

54.8 0.003765

54.9 0.003748

55 0.003731

55.1 0.003714

55.2 0.003697

55.3 0.003681

55.4 0.00366455.5 0.003647

55.6 0.003631

55.7 0.003614

55.8 0.003598

55.9 0.003582

56 0.003565

56.1 0.003549

56.2 0.003533

56.3 0.003517

56.4 0.003501

56.5 0.003485

56.6 0.003469

56.7 0.003454

56.8 0.003438

56.9 0.003422

57 0.003407

57.1 0.003391

57.2 0.003376

57.3 0.003361

57.4 0.003346

57.5 0.0033357.6 0.003315

57.7 0.0033

57.8 0.003285

57.9 0.00327

58 0.003256

58.1 0.003241

58.2 0.003226

58.3 0.003211

58.4 0.003197

58.5 0.003182

58.6 0.00316858.7 0.003154

58.8 0.003139

58.9 0.003125

59 0.003111

59.1 0.003097

59.2 0.003083

59.3 0.003069

59.4 0.003055


314/331

59.5 0.003041

59.6 0.003027

59.7 0.003013

59.8 0.003

59.9 0.002986

60 0.002973

60.1 0.00295960.2 0.002946

60.3 0.002932

60.4 0.002919

60.5 0.002906

60.6 0.002893

60.7 0.00288

60.8 0.002866

60.9 0.002853

61 0.002841

61.1 0.002828

61.2 0.002815

61.3 0.002802

61.4 0.002789

61.5 0.002777

61.6 0.002764

61.7 0.002752

61.8 0.002739

61.9 0.002727

62 0.002714

62.1 0.002702

62.2 0.0026962.3 0.002678

62.4 0.002665

62.5 0.002653

62.6 0.002641

62.7 0.002629

62.8 0.002617

62.9 0.002605

63 0.002594

63.1 0.002582

63.2 0.00257

63.3 0.00255963.4 0.002547

63.5 0.002535

63.6 0.002524

63.7 0.002512

63.8 0.002501

63.9 0.00249

64 0.002478

64.1 0.002467


315/331

64.2 0.002456

64.3 0.002445

64.4 0.002434

64.5 0.002423

64.6 0.002412

64.7 0.002401

64.8 0.0023964.9 0.002379

65 0.002368

65.1 0.002358

65.2 0.002347

65.3 0.002336

65.4 0.002326

65.5 0.002315

65.6 0.002305

65.7 0.002294

65.8 0.002284

65.9 0.002273

66 0.002263

66.1 0.002253

66.2 0.002243

66.3 0.002232

66.4 0.002222

66.5 0.002212

66.6 0.002202

66.7 0.002192

66.8 0.002182

66.9 0.00217267 0.002162

67.1 0.002153

67.2 0.002143

67.3 0.002133

67.4 0.002124

67.5 0.002114

67.6 0.002104

67.7 0.002095

67.8 0.002085

67.9 0.002076

68 0.00206668.1 0.002057

68.2 0.002048


316/331

63

66


317/331

For a particular Disney Ride, the mean time to

wait in line is 22 minutes (Distribution follows an

Exponential Distribution pattern.

mu 22 time to stand in line

x 15

P(x=25) 0.320984 =1-EXPONDIST(B6,1/B2,1)

P(15


318/331

3.1 0.03948

3.2 0.039301

3.3 0.039123

3.4 0.038946

3.5 0.038769

3.6 0.038593

3.7 0.0384183.8 0.038244

3.9 0.038071

4 0.037898

4.1 0.037726

4.2 0.037555

4.3 0.037385

4.4 0.037215

4.5 0.037046

4.6 0.036878

4.7 0.036711

4.8 0.036545

4.9 0.036379

5 0.036214

5.1 0.03605

5.2 0.035886

5.3 0.035723

5.4 0.035561

5.5 0.0354

5.6 0.035239

5.7 0.03508

5.8 0.0349215.9 0.034762

6 0.034605

6.1 0.034448

6.2 0.034291

6.3 0.034136

6.4 0.033981

6.5 0.033827

6.6 0.033674

6.7 0.033521

6.8 0.033369

6.9 0.0332177 0.033067

7.1 0.032917

7.2 0.032768

7.3 0.032619

7.4 0.032471

7.5 0.032324

7.6 0.032177

7.7 0.032031


319/331

7.8 0.031886

7.9 0.031741

8 0.031597

8.1 0.031454

8.2 0.031312

8.3 0.03117

8.4 0.0310288.5 0.030887

8.6 0.030747

8.7 0.030608

8.8 0.030469

8.9 0.030331

9 0.030193

9.1 0.030056

9.2 0.02992

9.3 0.029784

9.4 0.029649

9.5 0.029515

9.6 0.029381

9.7 0.029248

9.8 0.029115

9.9 0.028983

10 0.028852

10.1 0.028721

10.2 0.028591

10.3 0.028461

10.4 0.028332

10.5 0.02820310.6 0.028075

10.7 0.027948

10.8 0.027821

10.9 0.027695

11 0.02757

11.1 0.027445

11.2 0.02732

11.3 0.027196

11.4 0.027073

11.5 0.02695

11.6 0.02682811.7 0.026706

11.8 0.026585

11.9 0.026464

12 0.026344

12.1 0.026225

12.2 0.026106

12.3 0.025988

12.4 0.02587


320/331

12.5 0.025752

12.6 0.025636

12.7 0.025519

12.8 0.025404

12.9 0.025288

13 0.025174

13.1 0.0250613.2 0.024946

13.3 0.024833

13.4 0.02472

13.5 0.024608

13.6 0.024497

13.7 0.024385

13.8 0.024275

13.9 0.024165

14 0.024055

14.1 0.023946

14.2 0.023837

14.3 0.023729

14.4 0.023622

14.5 0.023515

14.6 0.023408

14.7 0.023302

14.8 0.023196

14.9 0.023091

15 0.022986

15.1 0.022882

15.2 0.02277815.3 0.

Date post:	03-Apr-2018
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