HSTAT1101 - Høst 2004

Tabell over normalfordelingen

(standardisert til forventning 0 og standardavvik 1)

Tabellen gir sannsynligheten P(Y < y) der Y er standard normalfordelt

Eksempel: P(Y < 0.23) = 0.5910

For negative tall kan du bruke: P(Y < - y) = 1 � P(Y < y)

 

 

y

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

 

 

 

 

 

 

 

 

 

 

 

0.0

.5000

.5040

.5080

.5120

.5160

.5199

.5239

.5279

.5319

.5359

0.1

.5398

.5438

.5478

.5517

.5557

.5596

.5636

.5675

.5714

.5753

0.2

.5793

.5832

.5871

.5910

.5948

.5987

.6026

.6064

.6103

.6141

0.3

.6179

.6217

.6255

.6293

.6331

.6368

.6406

.6443

.6480

.6517

0.4

.6554

.6591

.6628

.6664

.6700

.6736

.6772

.6808

.6844

.6879

0.5

.6915

.6950

.6985

.7019

.7054

.7088

.7123

.7157

.7190

.7224

0.6

.7257

.7291

.7324

.7357

.7389

.7422

.7454

.7486

.7517

.7549

0.7

.7580

.7611

.7642

.7673

.7703

.7734

.7764

.7794

.7823

.7852

0.8

.7881

.7910

.7939

.7967

.7995

.8023

.8051

.8078

.8106

.8133

0.9

.8159

.8186

.8212

.8238

.8264

.8289

.8315

.8340

.8365

.8389

 

 

 

 

 

 

 

 

 

 

 

1.0

.8413

.8438

.8461

.8485

.8508

.8531

.8554

.8577

.8599

.8621

1.1

.8643

.8665

.8686

.8708

.8729

.8749

.8770

.8790

.8810

.8830

1.2

.8849

.8869

.8888

.8907

.8925

.8944

.8962

.8980

.8997

.9015

1.3

.9032

.9049

.9066

.9082

.9099

.9115

.9131

.9147

.9162

.9177

1.4

.9192

.9207

.9222

.9236

.9251

.9265

.9279

.9292

.9306

.9319

1.5

.9332

.9345

.9357

.9370

.9382

.9394

.9406

.9418

.9429

.9441

1.6

.9452

.9463

.9474

.9484

.9495

.9505

.9515

.9525

.9535

.9545

1.7

.9554

.9564

.9573

.9582

.9591

.9599

.9608

.9616

.9625

.9633

1.8

.9641

.9649

.9656

.9664

.9671

.9678

.9686

.9693

.9699

.9706

1.9

.9713

.9719

.9726

.9732

.9738

.9744

.9750

.9756

.9761

.9767

 

 

 

 

 

 

 

 

 

 

 

2.0

.9772

.9778

.9783

.9788

.9793

.9798

.9803

.9808

.9812

.9817

2.1

.9821

.9826

.9830

.9834

.9838

.9842

.9846

.9850

.9854

.9857

2.2

.9861

.9864

.9868

.9871

.9875

.9878

.9881

.9884

.9887

.9890

2.3

.9893

.9896

.9898

.9901

.9904

.9906

.9909

.9911

.9913

.9916

2.4

.9918

.9920

.9922

.9925

.9927

.9929

.9931

.9932

.9934

.9936

2.5

.9938

.9940

.9941

.9943

.9945

.9946

.9948

.9949

.9951

.9952

2.6

.9953

.9955

.9956

.9957

.9959

.9960

.9961

.9962

.9963

.9964

2.7

.9965

.9966

.9967

.9968

.9969

.9970

.9971

.9972

.9973

.9974

2.8

.9974

.9975

.9976

.9977

.9977

.9978

.9979

.9979

.9980

.9981

2.9

.9981

.9982

.9982

.9983

.9984

.9984

.9985

.9985

.9986

.9986

 

 

 

 

 

 

 

 

 

 

 

3.0

.9987

.9987

.9987

.9988

.9988

.9989

.9989

.9989

.9990

.9990

3.1

.9990

.9991

.9991

.9991

.9992

.9992

.9992

.9992

.9993

.9993

3.2

.9993

.9993

.9994

.9994

.9994

.9994

.9994

.9995

.9995

.9995

3.3

.9995

.9995

.9995

.9996

.9996

.9996

.9996

.9996

.9996

.9997

3.4

.9997

.9997

.9997

.9997

.9997

.9997

.9997

.9997

.9997

.9998

3.5

.9998

.9998

.9998

.9998

.9998

.9998

.9998

.9998

.9998

.9998

 

Tabell over kjikvadratfordelingen

Tabellen gir sannsynligheten P(Z > z) der Z er kjikvadratfordelt og z er verdier i tabellen.

Eksempel: For kjikvadratfordelingen med 7 frihetsgrader has:

P(Z > 14.07) = 0.05

 

 

 

Sannsynlighet for � overstige angitt grense

Frihetsgrader

0.10

0.05

0.025

0.01

1

2.71

3.84

5.02

6.63

2

4.61

5.99

7.38

9.21

3

6.25

7.81

9.35

11.34

4

7.78

9.49

11.14

13.28

5

9.24

11.07

12.83

15.09

 

 

 

 

 

6

10.64

12.59

14.45

16.81

7

12.02

14.07

16.01

18.48

8

13.36

15.51

17.53

20.09

9

14.68

16.92

19.02

21.67

10

15.99

18.31

20.48

23.21

 

 

 

 

 

11

17.28

19.68

21.92

24.72

12

18.55

21.03

23.34

26.22

13

19.81

22.36

24.74

27.69

14

21.06

23.68

26.12

29.14

15

22.31

25.00

27.49

30.58

 

 

 

 

 

16

23.54

26.30

28.85

32.00

17

24.77

27.59

30.19

33.41

18

25.99

28.87

31.53

34.81

19

27.20

30.14

32.85

36.19

20

28.41

31.41

34.17

37.57

 

Tabell over Studentfordelingen

Tabellen gir sannsynligheten P(t > t0) der t er Studentfordelt

og t0 er et tall i tabellen.

Eksempel: For Studentfordelingen med 7 frihetsgrader has:

P(t > 1.895) = 0.05

 

 

 

Sannsynlighet for � overstige angitt grense

Frihetsgrader

0.25

0.10

0.05

0.025

0.01

0.005

1

1.000

3.078

6.314

12.706

31.821

63.657

2

0.816

1.886

2.920

4.303

6.965

9.925

3

0.765

1.638

2.353

3.182

4.541

5.841

4

0.741

1.533

2.132

2.776

3.747

4.604

 

 

 

 

 

 

 

5

0.727

1.476

2.015

2.571

3.365

4.032

6

0.718

1.440

1.943

2.447

3.143

3.707

7

0.711

1.415

1.895

2.365

2.998

3.499

8

0.706

1.397

1.860

2.306

2.896

3.355

9

0.703

1.383

1.833

2.262

2.821

3.250

 

 

 

 

 

 

 

10

0.700

1.372

1.812

2.228

2.764

3.169

11

0.697

1.363

1.796

2.201

2.718

3.106

12

0.695

1.356

1.782

2.179

2.681

3.055

13

0.694

1.350

1.771

2.160

2.650

3.012

14

0.692

1.345

1.761

2.145

2.624

2.977

 

 

 

 

 

 

 

15

0.691

1.341

1.753

2.131

2.602

2.947

16

0.690

1.337

1.746

2.120

2.583

2.921

17

0.689

1.333

1.740

2.110

2.567

2.898

18

0.688

1.330

1.734

2.101

2.552

2.878

19

0.688

1.328

1.729

2.093

2.539

2.861

 

 

 

 

 

 

 

20

0.687

1.325

1.725

2.086

2.528

2.845

21

0.686

1.323

1.721

2.080

2.518

2.831

22

0.686

1.321

1.717

2.074

2.508

2.819

23

0.685

1.319

1.714

2.069

2.500

2.807

24

0.685

1.318

1.711

2.064

2.492

2.797

 

 

 

 

 

 

 

25

0.684

1.316

1.708

2.06

2.485

2.787

26

0.684

1.315

1.706

2.056

2.479

2.779

27

0.684

1.314

1.703

2.052

2.473

2.771

28

0.683

1.313

1.701

2.048

2.467

2.763

29

0.683

1.311

1.699

2.045

2.462

2.756

 

 

 

 

 

 

 

30

0.683

1.310

1.697

2.042

2.457

2.750

40

0.681

1.303

1.684

2.021

2.423

2.704

60

0.679

1.296

1.671

2.000

2.390

2.660

120

0.677

1.289

1.658

1.980

2.358

2.617