formularios oficiales + tablas estadisticas - alejandro gonzalez (corregidos)

8/17/2019 Formularios oficiales + Tablas Estadisticas - Alejandro Gonzalez (Corregidos)

1/17

USACHFacultad de CienciaDpto. Matemática y CC.Área de Estadísticas

ALGUNOS MODELOS DE VARIABLES ALEATORIAS DISCRETAS

MODELO(Parámetros)

(*2)

FUNCIÓN DE CUANTÍA ESPERANZA VARIANZA ASIMETRÍA CURTOSIS F.GEN.M BERNOULLI

() −

0 , 1 1 2 3 16 BINOMIAL

(, ) ∈ +

−

0 , … , 1 2 3 16 GEOMÉTRICA

() − 1 , 2 , … 1 2 9 −

HIPERGEOMETRICA(,,) , ∈ +

{0 , } ≤ ≤ m i n {,}

1 . 115

PASCAL(, ) ∈ +

1 1 − , 1 , 2 , … 2 3 6 6 −

POISSON( )

> 0 − ! 0,1,2,… √ 3

1

− −

(*2) En todos los modelos con parámetro “”, se verifica 0 < < 1; 1 (*1) ; ; ;

Alejandro González Tapia - Ing. Civil en Minas


2/17

(*1) MODELO(Parámetros)

FUNCIÓN DE DENSIDADESPERANZA VARIANZA ASIMETRÍA CURTOSIS F.GEN.M

(*2) BETA(, ) > 0 , > 0

− 1 − 0 ≤ ≤ 1 1 (*2)

CHI-CUADRADO() > 0 − −

2 Γ 2 > 0 2 2√ 3 12 1 2 <

EXPONENCIAL( )

> 0 − > 0 1 1 2 9 1

−

< (*3) F-SNEDECOR

(, ) > 0 , > 0 − 1 −

+

> 0 2 > 2

2 2 24 > 4 GAMMA

(

, )

> 0 ,

> 0

− −

> 0

2√

3 6

1

−

< NORMAL(, ) ∞ < < ∞ ; > 0

1√ 2 −−

∞ < < ∞ 0 3 +

(*4) LOGNORMAL(, ) ∞ < < ∞ ; > 0

1√ 2 −l−

> 0 + (*4)

(*5) T-STUDENT() > 0 1

+

∞ < < ∞

0 2 > 2 0 32 4

UNIFORME(, ) < 1 ≤ ≤ 2 12 0 95 ≠ 0 (*6) WEIBULL

(, ) > 0 , > 0 −− > 0 Γ1 − (*6)

(*1) ; ; ;

(*2) :, ; ∫ 1 ;∞0 1! > 0 ; ∏ / −=(*3) 2 2 2

(*4) : [+][ 1] ; /

(*5) : 1/2√ /2 (*6) : (121)2(11) ; 1

ALGUNOS MODELOS DE VARIABLES ALEATORIAS CONTINUAS



3/17

INTERVALOS CONFIDENCIALES MÁS USUALES

Situación Parámetro Estimador Intervalo Confidencial del 1 100% X v.a. normal, una m.a. 1 −;−⁄ , 1 −;⁄ X v.a. normal, una m.a.

conocido ̅ ̅ −

√ , ̅ −

√

X v.a. normal, una m.a. desconocido ̅ ̅ −;− √ , ̅ −;− √ X v.a. Bernoulli ()

m.a. de tamaño n ̂ ̂ − ̂ , ̂ − ̂

X v.a. normal

dos m.a. independientes

−; −; ,

−; −;− X v.a. normal

dos m.a. independientes conocida ̅ ̅ ̅ ̅ ± − 1 1 X v.a. normal

dos m.a. independientes desconocida ̅ ̅ ̅ ̅ ± ;− 1 1

Con 2; −+−+− X v.a. normal

dos m.a. independientes

≠

desconocida

̅ ̅ ̅ ̅ ± ;−

Con g.l. (ver reverso)

X v.a. normal

dos m.a. pareadas ̅ ̅ −;− √ , ̅ −; √

(X,Y) ~ normal bivar. Usar gráfico ad_hoc −;−, −;−∗

∈ ~ 0, −;−, −;−∗

.. ± −;−.. 1 ̅ ∑ ̅ ± −;−.. 1 1 ̅ ∑ ̅

∗ .. 1 2 ( ) ; .. ∑ ̅ ; .. 1 ̅∑ ̅



4/17

DOCIMAS (BILATERALES) MÁS USUALES

Situación Hip. Nula Estadística Región Crítica

X v.a. normal, una m.a. 1 < −; ó > −;− X v.a. normal, una m.a.

conocido ̅

/√ < − ó > −

X v.a. normal, una m.a. desconocido ̅ /√ < −;− ó > −;− X v.a. Bernoulli ()

m.a. de tamaño n ̂ / < − ó > −

X v.a. normal

dos m.a. independientes < −; −; ó > −; −;− X v.a. normal

dos m.a. independientes conocidas ̅ ̅ 1/ 1/ < − ó > −

X v.a. normal

dos m.a. independientes desconocidas ̅ ̅ 1/ 1/ < ;− ó > ;−

Con 2; −+−+− X v.a. normal

dos m.a. independientes ≠ desconocidas(Problemas de Berens-Fisher)

̅ ̅ < ;− ó > ;−

Con + +

X v.a. normal

dos m.a. pareadas 0 ̅ ̅ √ < −;− ó > −;−

(X,Y) ~ normal bivar.

0

√ 2√ 1

< −;− ó > −;−

0 ∗

< −;− ó > −;− ∈ ~ 0, 0

∗ < −;− ó > −;−

∗ .. 1 2 ( ) ; .. ∑ ̅ ; .. 1 ̅∑ ̅



5/17

Variables Aleatorias Bidimensionales

Definición: Sean (X, Y) dos variables aleatorias discretas, entonces existe:

,, , ; ∀ , ∈ , llamada Distribución de Probabilidad Conjunta de X, Y)o función de cuantía conjunta de (X, Y) tal que cumple con:

1. 0 ≤ , ≤ 1 ∀, ∈ , 2 . ∑ ∑ , 1 Definición: Sean (X,Y) dos variables aleatorias continuas, entonces existe: ,, llamada función de densidad conjunta de (X, Y), tal cumple con:

1., ≥ 0; ∀, ∈ , 2 . ∫ ∫ ,

1

3. ≤ ≤ ; ≤ ≤ ∫ ∫ , = = Definición: Sean X e Y dos variables aleatorias discretas, tal que P(x,y) es su función de probabilidad

conjunta, entonces:

∑ ,, ; ∀∈ Distribución de probabilidad Marginal de X

∑ ,, ; ∀ ∈ Distribució

n de probabilidad Marginal de Y

/ ,, , ; ∀, ∈ , Distribución de probabilidad de X condicionada por Y / ,, , ; ∀, ∈ , Distribución de probabilidad de Y condicionada por X ( ⁄ ) ∑ ∙ ( ⁄ ) Esperanza de X condicionada por Y

( ⁄ ) (

) [( ⁄ )]

Varianza de X condicionada por Y

, { } Covarianza de X, Y ∑ ∑ ∙ ,, Esperanza conjunta de X, Y , , ; 1 ≤ , ≤ 1 Coeficiente de correlación de Pearson de X, Y ≤ ⁄ ≤ , Si X e Y son Variables aleatorias Discretas

UNIVERSIDAD DE SANTIAGO DE CHILE

FACULTAD DE CIENCIA

DEPTO. MAT y CIENCIA de la COMP

AREA de ESTADISTICA


6/17

Definición: Sean X e Y dos variables aleatorias continuas, tal que f(x,y) es su función de densidad conjunta,

entonces:

∫ ,

; ∀∈ Función de densidad Marginal de X ∫ ,

; ∀∈ Función de densidad Marginal de Y ⁄ , | ; ∀∈ Función de densidad de X condicionada por ⁄ , | ; ∀ ∈ Función de densidad de Y condicionada por Por lo tanto:

, ∙ ⁄ ∙ / ≤ ⁄ ∫ ⁄ = −∞

( ⁄ ) ∫ ⁄ Esperanza de X condicionada por ( ⁄ ) ( ) [( ⁄ )] Varianza de X condicionada por ∫ ∫ ∙ ∙ ,

Esperanza conjunta de X, Y

Propiedades de Covarianza

1. , ; ,

2. + , + , , , , ∈

3. + , + + + + , , , , ∈ Definición: Se dice que (X,Y) son variables aleatorias Independientes si y solo si:

, ∀, ∈ , Si X e Y son v. a. Discretas , ∀, ∈ , Si X e Y son v. a. Continuas Consecuencias: Si X e Y son variables aleatorias Independientes, entonces:

+ + , 0 + + +2 , + , 0 + 2 , +

/ ; / / ; / ~ ; y sea ~ ; entonces: + ~ + ; + ~ ; + Profesoras: Alma PlacenciaRosa Montaño

Ayudante: Alejandro Gonzá


7/17

-3.5-3.4-3.3

-3.2-3.1-3.0

-2.9-2.8-2.7-2.6-2.5-2.4-2.3-2.2-2.1-2.0

-1.9-1.8-1.7-1.6

-1.5-1.4-1.3-1.2-1.1-1.0

-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.1-0.0

0.0

0.10.20.30.40.50.60.70.80.9

1.01.11.21.31.41.51.61.71.8

1.92.02.12.22.32.42.52.62.72.82.9

3.03.13.23.33.43.5

.00

0.00020.00030.0005

0.00070.00100.0013

0.00190.00260.00350.00470.00620.00820.01070.01390.01790.0228

0.02870.03590.04460.0548

0.06680.08080.09680.11510.13570.1587

0.18410.21190.24200.27430.30850.34460.38210.42070.46020.5000

0.5000

0.53980.57930.61790.65540.69150.72570.75800.78810.8159

0.84130.86430.88490.90320.91920.93320.94520.95540.9641

0.97130.97720.98210.98610.98930.99180.99380.99530.99650.99740.9981

0.99870.99900.99930.99950.99970.9998

.01

0.00020.00030.0005

0.00070.00090.0013

0.00180.00250.00340.00450.00600.00800.01040.01360.01740.0222

0.02810.03510.04360.0537

0.06550.07930.09510.11310.13350.1562

0.18140.20900.23890.27090.30500.34090.37830.41680.45620.4960

0.5040

0.54380.58320.62170.65910.69500.72910.76110.79100.8186

0.84380.86650.88690.90490.92070.93450.94630.95640.9649

0.97190.97780.98260.98640.98960.99200.99400.99550.99660.99750.9982

0.99870.99910.99930.99950.99970.9998

.02

0.00020.00030.0005

0.00060.00090.0013

0.00180.00240.00330.00440.00590.00780.01020.01320.01700.0217

0.02740.03440.04270.0526

0.06430.07780.09340.11120.13140.1539

0.17880.20610.23580.26760.30150.33720.37450.41290.45220.4920

0.5080

0.54780.58710.62550.66280.69850.73240.76420.79390.8212

0.84610.86860.88880.90660.92220.93570.94740.95730.9656

0.97260.97830.98300.98680.98980.99220.99410.99560.99670.99760.9982

0.99870.99910.99940.99950.99970.9998

.03

0.00020.00030.0004

0.00060.00090.0012

0.00170.00230.00320.00430.00570.00750.00990.01290.01660.0212

0.02680.03360.04180.0516

0.06300.07640.09180.10930.12920.1515

0.17620.20330.23270.26430.29810.33360.37070.40900.44830.4880

0.5120

0.55170.59100.62930.66640.70190.73570.76730.79670.8238

0.84850.87080.89070.90820.92360.93700.94840.95820.9664

0.97320.97880.98340.98710.99010.99250.99430.99570.99680.99770.9983

0.99880.99910.99940.99960.99970.9998

.04

0.00020.00030.0004

0.00060.00080.0012

0.00160.00230.00310.00410.00550.00730.00960.01250.01620.0207

0.02620.03290.04090.0505

0.06180.07490.09010.10750.12710.1492

0.17360.20050.22970.26110.29460.33000.36690.40520.44430.4840

0.5160

0.55570.59480.63310.67000.70540.73890.77030.79950.8264

0.85080.87290.89250.90990.92510.93820.94950.95910.9671

0.97380.97930.98380.98750.99040.99270.99450.99590.99690.99770.9984

0.99880.99920.99940.99960.99970.9998

.05

0.00020.00030.0004

0.00060.00080.0011

0.00160.00220.00300.00400.00540.00710.00940.01220.01580.0202

0.02560.03220.04010.0495

0.06060.07350.08850.10560.12510.1469

0.17110.19770.22660.25780.29120.32640.36320.40130.44040.4801

0.5199

0.55960.59870.63680.67360.70880.74220.77340.80230.8289

0.85310.87490.89440.91150.92650.93940.95050.95990.9678

0.97440.97980.98420.98780.99060.99290.99460.99600.99700.99780.9984

0.99890.99920.99940.99960.99970.9998

.06

0.00020.00030.0004

0.00060.00080.0011

0.00150.00210.00290.00390.00520.00690.00910.01190.01540.0197

0.02500.03140.03920.0485

0.05940.07210.08690.10380.12300.1446

0.16850.19490.22360.25460.28770.32280.35940.39740.43640.4761

0.5239

0.56360.60260.64060.67720.71230.74540.77640.80510.8315

0.85540.87700.89620.91310.92790.94060.95150.96080.9686

0.97500.98030.98460.98810.99090.99310.99480.99610.99710.99790.9985

0.99890.99920.99940.99960.99970.9998

.07

0.00020.00030.0004

0.00050.00080.0011

0.00150.00210.00280.00380.00510.00680.00890.01160.01500.0192

0.02440.03070.03840.0475

0.05820.07080.08530.10200.12100.1423

0.16600.19220.22060.25140.28430.31920.35570.39360.43250.4721

0.5279

0.56750.60640.64430.68080.71570.74860.77940.80780.8340

0.85770.87900.89800.91470.92920.94180.95250.96160.9693

0.97560.98080.98500.98840.99110.99320.99490.99620.99720.99790.9985

0.99890.99920.99950.99960.99970.9998

.08

0.00020.00030.0004

0.00050.00070.0010

0.00140.00200.00270.00370.00490.00660.00870.01130.01460.0188

0.02390.03010.03750.0465

0.05710.06940.08380.10030.11900.1401

0.16350.18940.21770.24830.28100.31560.35200.38970.42860.4681

0.5319

0.57140.61030.64800.68440.71900.75170.78230.81060.8365

0.85990.88100.89970.91620.93060.94290.95350.96250.9699

0.97610.98120.98540.98870.99130.99340.99510.99630.99730.99800.9986

0.99900.99930.99950.99960.99970.9998

.09

0.0000.0000.000

0.0000.0000.001

0.0010.0010.0020.0030.0040.0060.0080.0110.0140.018

0.0230.0290.0360.045

0.0550.0680.0820.0980.1170.137

0.1610.1860.2140.2450.2770.3120.3480.3850.4240.464

0.535

0.5750.6140.6510.6870.7220.7540.7850.8130.838

0.8620.8830.9010.9170.9310.9440.9540.9630.970

0.9760.9810.9850.9890.9910.9930.9950.9960.9970.9980.998

0.9990.9990.9990.9990.9990.999

TABLA D Valores de la función de distribución acumulativa normal estándarTABLA D Valores de la función de distribución acumulativa normal estándar

< = ;, = −

−∞

TABLAS DE ESTADIST1CA$150.- CODIGO VENTA 381

Profesor: SEGUNDO KARL B.Ayudante: ALEJANDRO GONZÁLEZ


8/17

0

12345

6789

10

1112131415

16

17181920

2122232425

2627282930

3132

333435

3637383940

4142434445

464748

4950

5152535455

5657585960

0.005

-0.0100.0720.2070.412

0.6760.9891.3441.7352.156

2.6033.0743.5654.0754.601

5.142

5.6976.2656.8447.434

8.0348.6439.2609.886

10.520

11.16011.80812.46113.12113.787

14.45815.134

15.81516.50117.192

17.88718.58619.28919.99620.707

21.42122.13822.85923.58424.311

25.04125.77526.511

27.24927.991

28.73529.48130.23030.98131.735

32.49033.24834.00834.77035.534

0.01

-0.0200.1150.2970.554

0.8721.2391.6462.0882.558

3.0533.5714.1074.6605.229

5.812

6.4087.0157.6338.260

8.8979.542

10.19610.85611.524

12.19812.87913.56514.25714.954

15.65516.362

17.07417.78918.509

19.23319.96020.69121.42622.164

22.90623.65024.39825.14825.901

26.65727.41628.177

28.94129.707

30.47531.24632.01832.79333.570

34.35035.13135.91336.69837.485

0.025

0.0010.0510.2160.4840.831

1.2371.6902.1802.7003.247

3.8164.4045.0095.6296.262

6.908

7.5648.2318.9079.591

10.28310.98211.68912.40113.120

13.84414.57315.30816.04716.791

17.53918.291

19.04719.80620.569

21.33622.10622.87823.65424.433

25.21525.99926.78527.57528.366

29.16029.95630.755

31.55532.357

33.16233.96834.77635.58636.398

37.21238.02738.84439.66240.482

0.05

0.0040.1030.3520.7111.145

1.6352.1672.7333.3253.940

4.5755.2265.8926.5717.261

7.962

8.6729.39010.11710.851

11.59112.33813.09113.84814.611

15.37916.15116.92817.70818.493

19.28120.072

20.86721.66422.465

23.26924.07524.88425.69526.509

27.32628.14428.96529.78730.612

31.43932.26833.098

33.93034.764

35.60036.43737.27638.11638.958

39.80140.64641.49242.33943.188

0.10

0.0160.2110.5841.0641.610

2.2042.8333.4904.1684.865

5.5786.3047.0427.7908.547

9.312

10.08510.86511.65112.443

13.24014.04214.84815.65916.473

17.29218.11418.93919.76820.599

21.43422.271

23.11023.95224.797

25.64326.49227.34328.19629.051

29.90730.76531.62532.48733.350

34.21535.08135.949

36.81837.689

38.56039.43340.30841.18342.060

42.93743.81644.69645.57746.459

0.25

0.1020.5751.2131.9232.675

3.4554.2555.0715.8996.737

7.5848.4389.299

10.16511.037

11.912

12.79213.67514.56215.452

16.34417.24018.13719.03719.939

20.84321.74922.65723.56724.478

25.39026.304

27.21928.13629.054

29.97330.89331.81532.73733.660

34.58535.51036.43637.36338.291

39.22040.14941.079

42.01042.942

43.87444.80845.74146.67647.610

48.54649.48250.41951.35652.294

0.75

1.3292.7734.1085.3856.626

7.8419.037

10.21911.38912.549

13.70114.84515.98417.11718.245

19.369

20.48921.60522.71823.828

24.93526.03927.14128.24129.339

30.43531.52832.62033.71134.800

35.88736.973

38.05839.14140.223

41.30442.38343.46244.53945.616

46.69247.76648.84049.91350.985

52.05653.12754.196

55.26556.334

57.40158.46859.53460.60061.665

62.72963.79364.85765.91966.981

0.90

2.7064.6056.2517.7799.236

10.64512.01713.36214.68415.987

17.27518.54919.81221.06422.307

23.542

24.76925.98927.20428.412

29.61530.81332.00733.19634.382

35.56336.74137.91639.08740.256

41.42242.585

43.74544.90346.059

47.21248.36349.51350.66051.805

52.94954.09055.23056.36957.505

58.64159.77460.907

62.03863.167

64.29565.42266.54867.67368.796

69.91971.04072.16073.27974.397

0.95

3.8415.9917.8159.488

11.071

12.59214.06715.50716.91918.307

19.67521.02622.36223.68524.996

26.296

27.58728.86930.14431.410

32.67133.92435.17236.41537.652

38.88540.11341.33742.55743.773

44.98546.194

47.40048.60249.802

50.99852.19253.38454.57255.758

56.94258.12459.30460.48161.656

62.83064.00165.171

66.33967.505

68.66969.83270.99372.15373.311

74.46875.62476.77877.93179.082

0.975

5.0247.3789.348

11.14312.833

14.44916.01317.53519.02320.483

21.92023.33724.73626.11927.488

28.845

30.19131.52632.85234.170

35.47936.78138.07639.36440.646

41.92343.19444.46145.72246.979

48.23249.480

50.72551.96653.203

54.43755.66856.89658.12059.342

60.56161.77762.99064.20165.410

66.61767.82169.023

70.22271.420

72.61673.81075.00276.19277.380

78.56779.75280.93682.11783.298

0.99

6.6359.210

11.34513.27715.086

16.81218.47520.09021.66623.209

24.72526.21727.68829.14130.578

32.000

33.40934.80536.19137.566

38.93240.28941.63842.98044.314

45.64246.96348.27849.58850.892

52.19153.486

54.77656.06157.342

58.61959.89261.16262.42863.691

64.95066.20667.45968.71069.957

71.20172.44373.683

74.91976.154

77.38678.61679.84381.06982.292

83.51384.73385.95087.16688.379

1111

12222

22233

3

3333

44444

44555

55

556

66666

66777

777

77

88888

88899

VALORES PERCENTILES, , DE LA DISTRIBUCIÓNCON GRADOS DE LIBERTAD

1 −

Pág. 2


9/17

01

6162636465

6667686970

7172737475

7677787980

8182838485

86

87888990

9192939495

96979899

100

102104

106108110

112114116118120

122124126128130

132134136

138140

142144146148150

200250300400500

600700800900

1000

0.0051

36.30037.06837.83838.61039.383

40.15840.93541.71342.49443.275

44.05844.84345.62946.41747.206

47.99748.78849.58250.37651.172

51.96952.76753.56754.36855.170

55.973

56.77757.58258.38959.196

60.00560.81561.62562.43763.250

64.06364.87865.69466.51067.328

68.96570.606

72.25173.89975.550

77.20478.86280.52282.18583.852

85.52087.19288.86690.54392.222

93.90495.58897.275

98.964100.655

102.348104.044105.741107.441109.142

152.241196.161240.663330.903422.303

514.529607.380700.725794.475

888.564

0.011

38.27339.06339.85540.64941.444

42.24043.03843.83844.63945.442

46.24647.05147.85848.66649.475

50.28651.09751.91052.72553.540

54.35755.17455.99356.81357.634

58.456

59.27960.10360.92861.754

62.58163.40964.23865.06865.898

66.73067.56268.39669.23070.065

71.73773.413

75.09276.77478.458

80.14681.83683.52985.22586.923

88.62490.32792.03393.74195.451

97.16398.878

100.595

102.314104.034

105.757107.482109.209110.937112.668

156.432200.939245.972337.155429.388

522.365615.907709.897804.252

898.912

0.0251

41.03842.12642.95043.77644.603

45.43146.26147.09247.92448.758

49.59250.42851.26552.10352.942

53.78254.62355.46656.30957.153

57.99858.84559.69260.54061.389

62.239

63.08963.94164.79365.647

66.50167.35668.21169.06869.925

70.78371.64272.50173.36174.222

75.94677.672

79.40181.13382.867

84.60486.34288.08489.82791.573

93.32095.07096.82298.576

100.331

102.089103.848105.609

107.372109.137

110.903112.671114.441116.212117.985

162.728208.098253.912346.482439.936

534.019628.577723.513818.756

914.257

0.051

44.03844.88945.74146.77647.450

48.30549.16250.02050.87951.739

52.60053.46254.32555.18956.054

56.92057.78658.65459.52260.391

61.26162.13263.00463.87664.749

65.623

66.49867.37368.24969.126

70.00370.88271.76072.64073.520

74.40175.28276.16477.04677.929

79.69781.468

83.24085.01586.792

88.57090.35192.13493.91895.705

97.49399.283

101.074102.867104.662

106.459108.257110.056

111.857113.659

115.463117.268119.075120.883122.692

168.279214.392260.878354.641449.147

544.180639.613735.362831.370

927.594

0.101

47.34248.22649.11149.99650.883

51.77052.65953.54854.43855.329

56.22157.11358.00658.90059.795

60.69061.58662.48363.38064.278

65.17666.07666.97667.87668.777

69.679

70.58171.48472.38773.291

74.19675.10076.00676.91277.818

78.72579.63380.54181.44982.358

84.17785.998

87.82189.64591.471

93.29995.12896.95898.790

100.624

102.458104.295106.132107.971109.811

111.652113.495115.338

117.183119.029

120.876122.724124.574126.424128.275

174.835221.806269.068364.207459.926

556.056652.497749.185846.075

943.133

0.251

53.23254.17155.11056.05056.990

57.93158.87259.81460.75661.698

62.64163.58564.52865.47266.417

67.36268.30769.25270.19871.145

72.09173.03873.98574.93375.881

76.829

77.77778.72679.67580.625

81.57482.52483.47484.42585.376

86.32787.27888.22989.18190.133

92.03893.944

95.85097.75899.666

101.575103.485105.396107.307109.220

111.133113.046114.961116.876118.792

120.708122.625124.543

126.461128.380

130.299132.219134.140136.061137.983

186.172234.577283.135380.577478.323

576.286674.413772.669871.032

969.484

0.751

68.04369.10470.16571.22572.285

73.34474.40375.46176.51977.577

78.63479.69080.74781.80382.858

83.91384.96886.02287.07788.130

89.18490.23791.28992.34293.394

94.449

95.49796.54897.59998.650

99.700100.750101.800102.850103.899

104.948105.997107.045108.093109.141

111.236113.331

115.424117.517119.608

121.699123.789125.878127.967130.055

132.142134.228136.313138.398140.482

142.566144.649146.731

148.813150.894

152.975155.055157.134159.213161.291

213.102264.697316.138418.697520.950

622.988724.861826.604928.241

1029.790

0.901

75.51476.63077.74578.86079.973

81.08582.19783.30884.41885.527

86.63587.74388.85089.95691.061

92.16693.27094.37495.47696.578

97.68098.78099.880

100.980102.079

103.177

104.275105.372106.469107.565

108.661109.756110.850111.944113.038

114.131115.223116.315117.407118.498

120.679122.856

125.035127.211129.385

131.558133.729135.898138.066140.233

142.398144.562146.724148.885151.045

153.204155.361157.518

159.673161.827

163.980166.132168.283170.432172.581

226.021279.050331.789436.649540.930

644.800748.359851.671954.782

1057.724

0.951

80.23281.38182.52983.67584.821

85.96587.10888.25089.39190.531

91.67092.80893.94595.08196.217

97.35198.48499.617

100.749101.879

103.010104.139105.267106.395107.522

108.648

109.773110.898112.022113.145

114.268115.390116.511117.632118.752

119.871120.990122.108123.225124.342

126.574128.804

131.031133.257135.480

137.701139.921142.138144.354146.567

148.779150.989153.198155.405157.610

159.814162.016164.216

166.415168.613

170.809173.004175.198177.390179.581

233.994287.882341.395447.632553.127

658.094762.661866.911970.904

1074.679

0.9751

84.47685.65486.83088.00489.177

90.34991.51992.68993.85695.023

96.18997.35398.51699.678

100.839

101.999103.158104.316105.473106.629

107.783108.937110.090111.242112.393

113.544

114.693115.841116.989118.136

119.282120.427121.571122715

123.858

125.000126.141127.282128.422129.561

131.838134.111

136.382138.651140.917

143.180145.441147.700149.957152.211

154.464156.714158.962161.209163.453

165.696167.936170.175

172.412174.648

176.882179.114181.344183.573185.800

241.058295.689349.874457.305563.852

669.769775.211880.275985.032

1089.531

0.991

89.59190.80292.01093.21794.422

95.62696.82898.02899.228

100.425

101.621102.816104.010105.202106.393

107.583108.771109.958111.144112.329

113.512114.695115.876117.057118.236

119.414

120.591121.767122.942124.116

125.289126.462127.633128.803129.973

131.141132.309133.476134.642135.807

138.134140.459

142.780145.099147.414

149.727152.037154.344156.648158.950

161.250163.548165.841168.133170.423

172.711174.996177.280

179.561181.840

184.118186.393188.666190.938193.208

249.445304.940359.906468.724576.493

683.516789.974895.984

1001.630

1106.969

99999

910101010

1010101011

1111111111

1111111212

12

12121212

1213131313

1313131314

1414

141415

1515151616

1616171717

171718

1818

1819191919

2531364758

698090

101

111

1 −

Valores Percentiles, , de la Distribución . (Continuación). Pág. 3


10/17


11/17

0 . 9

9

2 . 3

6 8 0

2 . 3

6 7 6

2 . 3

4 7 1

2 . 3

6 6 7

2 . 3

6 6 2

2 . 3

6 5 8

2 . 3

6 5 4

2 . 3

6 5 0

2 . 3

6 4 6

2 . 3

6 4 2

2 . 3

6 3 5

2 . 3

6 2 7

2 . 3

6 2 0

2 . 3

6 1 4

2 . 3

6 0 7

2 . 3

6 0 1

2 . 3

5 9 5

2 . 3

5 8 9

2 . 3

5 8 4

2 . 3

5 7 8

2 . 3

5 7 3

2 . 3

5 6 8

2 . 3

5 6 3

2 . 3

5 5 8

2 . 3

5 5 4

2 . 3

5 4 9

2 . 3

5 4 5

2 . 3

5 4 1

2 . 3

5 3 7

2 . 3

5 3 3

2 . 3

5 2 9

2 . 3

5 2 5

2 . 3

5 2 2

2 . 3

5 1 8

2 . 3

5 1 5

2 . 3

4 5 1

2 . 3

3 8 8

2 . 3

3 5 7

2 . 3

3 3 8

2 . 3

3 2 6

2 . 3

3 1 7

2 . 3

3 1 0

2 . 3

3 0 5

2 . 3

3 0 1

2 . 3

2 6 3

0 . 9

9 5

2 . 6

3 0 9

2 . 6

3 0 3

2 . 6

2 9 7

2 . 6

2 9 1

2 . 6

2 8 6

2 . 6

2 8 0

2 . 6

2 7 5

2 . 6

2 6 9

2 . 6

2 6 4

2 . 6

2 5 9

2 . 6

2 4 9

2 . 6

2 3 9

2 . 6

2 3 0

2 . 6

2 2 1

2 . 6

2 1 3

2 . 6

2 0 4

2 . 6

1 9 6

2 . 6

1 8 9

2 . 6

1 8 1

2 . 6

1 7 4

2 . 6

1 6 7

2 . 6

1 6 1

2 . 6

1 5 4

2 . 6

1 4 8

2 . 6

1 4 2

2 . 6

1 3 6

2 . 6

1 3 0

2 . 6

1 2 5

2 . 6

1 1 9

2 . 6

1 1 4

2 . 6

1 0 9

2 . 6

1 0 4

2 . 6

0 9 9

2 . 6

0 9 5

2 . 6

0 9 0

2 . 6

0 0 6

2 . 5

9 2 3

2 . 5

8 8 2

2 . 5

8 5 7

2 . 5

8 4 0

2 . 5

8 2 9

2 . 5

8 2 0

2 . 5

8 1 3

2 . 5

8 0 6

2 . 5

7 5 8

0 . 7

5

0 . 6

7 7 2

0 . 6

7 7 2

0 . 6

7 7 1

0 . 6

7 7 1

0 . 6

7 7 1

0 . 6

7 7 1

0 . 6

7 7 0

0 . 6

7 7 0

0 . 6

7 7 0

0 . 6

7 7 0

0 . 6

7 6 9

0 . 6

7 6 9

0 . 6

7 6 8

0 . 6

7 6 8

0 . 6

7 6 7

0 . 6

7 6 7

0 . 6

7 6 6

0 . 6

7 6 6

0 . 6

7 6 6

0 . 6

7 6 5

0 . 6

7 6 5

0 . 6

7 6 5

0 . 6

7 6 4

0 . 6

7 6 4

0 . 6

7 6 4

0 . 6

7 6 4

0 . 6

7 6 3

0 . 6

7 6 3

0 . 6

7 6 3

0 . 6

7 6 2

0 . 6

7 6 2

0 . 6

7 6 2

0 . 6

7 6 2

0 . 6

7 6 2

0 . 6

7 6 1

0 . 6

7 5 7

0 . 6

7 5 3

0 . 6

7 5 1

0 . 6

7 5 0

0 . 6

7 4 9

0 . 6

7 4 8

0 . 6

7 4 8

0 . 6

7 4 8

0 . 6

7 4 7

0 . 6

7 4 5

9 1

9 2

9 3

9 4

9 5

9 6

9 7

9 8

9 9

1 0 0

1 0 2

1 0 4

1 0 6

1 0 8

1 1 0

1 1 2

1 1 4

1 1 6

1 1 8

1 2 0

1 2 2

1 2 4

1 2 6

1 2 8

1 3 0

1 3 2

1 3 4

1 3 6

1 3 8

1 4 0

1 4 2

1 4 4

1 4 6

1 4 8

1 5 0

2 0 0

3 0 0

4 0 0

5 0 0

6 0 0

7 0 0

8 0 0

9 0 0

1 0 0 0

∞

1

−

0 . 9

0

1 . 2

9 0 9

1 . 2

9 0 8

1 . 2

9 0 7

1 . 2

9 0 6

1 . 2

9 0 5

1 . 2

9 0 4

1 . 2

9 0 3

1 . 2

9 0 2

1 . 2

9 0 2

1 . 2

9 0 1

1 . 2

8 9 9

1 . 2

8 9 7

1 . 2

9 9 6

1 . 2

8 9 4

1 . 2

8 9 3

1 . 2

8 9 2

1 . 2

8 9 0

1 . 2

8 8 9

1 . 2

8 8 8

1 . 2

8 8 6

1 . 2

8 8 5

1 . 2

8 8 4

1 . 2

8 8 3

1 . 2

8 8 2

1 . 2

8 8 1

1 . 2

8 8 0

1 . 2

8 7 9

1 . 2

8 7 8

1 . 2

8 7 7

1 . 2

8 7 6

1 . 2

8 7 5

1 . 2

8 7 5

1 . 2

8 7 4

1 . 2

8 7 3

1 . 2

8 7 2

1 . 2

8 5 8

1 . 2

8 4 4

1 . 2

8 3 7

1 . 2

8 3 2

1 . 2

8 3 0

1 . 2

8 2 8

1 . 2

8 2 6

1 . 2

8 2 5

1 . 2

8 2 4

1 . 2

8 1 6

0 . 9

5

1 . 6

6 1 8

1 . 6

6 1 6

1 . 6

6 1 4

1 . 6

6 1 2

1 . 6

6 1 1

1 . 6

6 0 9

1 . 6

6 0 7

1 . 6

6 0 6

1 . 6

6 0 4

1 . 6

6 0 2

1 . 6

5 9 9

1 . 6

5 9 6

1 . 6

5 9 4

1 . 6

5 9 1

1 . 6

5 8 8

1 . 6

5 8 6

1 . 6

5 8 3

1 . 6

5 8 1

1 . 6

5 7 9

1 . 6

5 7 7

1 . 6

5 7 4

1 . 6

5 7 2

1 . 6

5 7 0

1 . 6

5 6 8

1 . 6

5 6 7

1 . 6

5 6 5

1 . 6

5 6 3

1 . 6

5 6 1

1 . 6

5 6 0

1 . 6

5 5 8

1 . 6

5 5 7

1 . 6

5 5 5

1 . 6

5 5 4

1 . 6

5 5 2

1 . 6

5 5 1

1 . 6

5 2 5

1 . 6

4 9 9

1 . 6

4 8 7

1 . 6

4 7 9

1 . 6

4 7 4

1 . 6

4 7 0

1 . 6

4 6 8

1 . 6

4 6 5

1 . 6

4 6 4

1 . 6

4 4 9

0 . 9

7 5

1 . 9

8 6 4

1 . 9

8 6 1

1 . 9

8 5 8

1 . 9

8 5 5

1 . 9

8 5 3

1 . 9

8 5 0

1 . 9

8 4 7

1 . 9

8 4 5

1 . 9

8 4 2

1 . 9

8 4 0

1 . 9

8 3 5

1 . 9

8 3 0

1 . 9

8 2 6

1 . 9

8 2 2

1 . 9

8 1 8

1 . 9

8 1 4

1 . 9

8 1 0

1 . 9

8 0 6

1 . 9

8 0 3

1 . 9

7 9 9

1 . 9

7 9 6

1 . 9

7 9 3

1 . 9

7 9 0

1 . 9

7 8 7

1 . 9

7 8 4

1 . 9

7 8 1

1 . 9

7 7 8

1 . 9

7 7 6

1 . 9

7 7 3

1 . 9

7 7 1

1 . 9

7 6 8

1 . 9

7 6 6

1 . 9

7 6 3

1 . 9

7 6 1

1 . 9

7 5 9

1 . 9

7 1 9

1 . 9

6 7 9

1 . 9

6 5 9

1 . 9

6 4 7

1 . 9

6 3 9

1 . 9

6 3 4

1 . 9

6 2 9

1 . 9

6 2 6

1 . 9

6 2 3

1 . 9

6 0 0

1

−

Pág.


12/17

.500

.750

.9001 .950

.975

.990

.995

.500

.750

.9002 .950

.975

.990.995

.500

.750

.9003 .950

.975

.990

.995

.500

.750

.9004 .950

.975

.990

.995

.500

.750.9005 .950

.975

.990

.995

.500

.750

.9006 .950

.975

.990

.995

.500

.750

.9007 .950

.975

.990

.995

.500

.750

.9008 .950

.975

.990

.995

.500

.750

.9009 .950

.975

.990

.995

.500

.750

.90010 .950

.975

.990

.995

.500

.750

.90011 .950

.975

.990

.995

.500

.750

.90012 .950

.975

.990

.995

1

1.00005.828539.864161.45647.794052.216211

.666672.57148.526318.51338.506

98.503198.50

.585062.02395.538310.12817.44334.11655.552

.548631.80744.54487.708612.21821.19831.333

.52807

1.69254.06046.607910.00716.25822.785

.514891.62143.77605.98748.8131

13.74518.635

.505721.57323.58945.59148.072712.24616.236

.498981.53843.45795.31777.570911.25914.688

.493821.51213.36035.11747.209310.56113.814

.489731.4915

3.28504.96466.936710.04412.826

.486441.47493.22524.84436.72419.646012.226

.483691.46133.17654.74726.55389.3302

11 .754

2

1.50007.500049.500199.50799.504999.520000

1.00003.00009.000019.00039.000

99.000199.00

.881102.27985.46249.552116.04430.81749.799

.828432.00004.32466.944310.64918.00026.284

.79877

1.85281.77975.78618.433613.27418.314

.779761.76223.46335.14337.259810.92514.544

.766551.70103.25744.73746.54159.546612.404

.756831.65693.11314.45906.05958.649111.042

.749381.62363.00654.25655.71478.021510.107

.743491.5975

2.92454.10285.45647.53949.4772

.738721.57672.85953.98235.25557.20578.9122

.734771.55952.80653.88535.09596.9265

8.5095

3

1.70928.199953.593215.71864.165403.321615

1.13493.15349.161819.16439.165

99.166199.17

1.00002.35555.39089.276615.43929.45747.467

.940542.04674.19086.59149.979216.69424.259

.90715

1.88433.61955.40957.763612.06016.530

.885781.78443.28884.75716.59889.779512.917

.870951.71693.07414.34685.85988.451310.882

.860041.66832.92384.06625.41607.59109.5965

.851681.63152.81293.86265.07816.99198.7171

.845081.6028

2.72773.70834.82566.55238.0807

.839731.57982.66023.56744.63006.21677.6004

.835301.56092.60553.49034.47425.9526

7.2258

4

1.82278.581055.883224.58899.585624.622500

1.20713.23209.243419.24739.248

99.249199.25

1.06322.39015.34279.117215.10128.71046.195

1.00002.06424.10736.38839.604515.97723.155

.96456

1.89273.52025.19227.387911.39215.556

.941911.78723.18084.53376.22729.148312.028

.926191.71572.96054.12035.52267.846710.050

.914641.66422.80643.83785.05267.00608.8051

.905801.62532.69273.63314.71816.47217.9559

.898821.5949

2.60533.47804.46835.99437.3428

.893161.57042.53623.35674.27515.66836.8809

.888481.55032.48013.25924.12125.4119

6.5211

5

1.89378.819857.241230.16921.855763.723056

1.25193.27999.292619.29639.298

99.299199.30

1.10242.40955.30929.013514.88528.23745.392

1.03672.07234.05066.25609.364515.52222.456

1.0000

1.89473.45305.05037.146410.96714.940

.976541.78523.10754.38745.98768.745911.464

.960261.71112.88333.97155.28527.46049.5221

.948311.65752.72653.68754.81736.63188.3018

.939161.61702.61063.48174.48446.05697.4711

.931931.5853

2.52163.32584.23615.63636.8723

.926081.55982.45123.20394.04405.31606.4217

.921241.53892.39403.10593.89115.0643

6.0711

6

1.94228.983358.204233.99937.115859.023437

1.28243.31219.325519.33039.331

99.332199.33

1.12892.42185.28478.940614.73527.91144.838

1.06172.07664.00986.16319.197315.20721.975

1.0240

1.89453.40454.95036.977710.67214.513

1.00001.78213.05464.28395.81978.466111.073

.983341.70592.82743.86605.11867.19149.1554

.971111.65082.66833.58064.65176.37077.9520

.961751.60912.55093.37384.31975.80187.1338

.954361.5765

2.46063.21724.07215.38586.5446

.948371.55022.38913.09463.88075.06926.1015

.943421.52862.33102.99613.72834.8206

5.7570

7

1.97749.102158.906

236.7 7948.225928.32373 5

1.30453.33529.349119.353

39. 355

99.356199.36

1.14822.43025.26628.886814.62427.67244.434

1.07972.07903.97906.09429.074114.976

21 .622

1.0414

1.89353.36794.87596.853110.45614.200

1.01691.77893.01454.20665.69558.260010.786

1.00001.70112.78493.78704.99496.99288.8854

.987571.64482.62413.50054.5286

6. 17767.6942

.978051.60222.50533.29274.19715.61296.8849

.970541.5688

2.41403.13553.94985.20016.3025

.964451.54182.34163.01233.75864.88615.8648

.959431 .51972.28282.91343.60654.6395

5.5245

8

2.00419.192259.439238.88956.665981.123925

1.32133.35269.366819.37139.373

99.374199.37

1.16272.43645.25178.845214.54027.48944.126

1.09332.08053.95496.04108.979614.79921.352

1.0545

1.89233.33934.81836.757210.28913.961

1.02981.77602.98304.14685.59968.101610.566

1.01261.69692.75163.72574.89946.84018.6781

1.00001.63962.58933.43814.43326.02897.4960

.990371.59612.46943.22964.10205.46716.6933

.982761.5621

2.37723.07173.85495.05676.1159

.976611.53462.30402.94803.66384.74455.6821

.971521.51202.24462.84863.51184.4994

5.3451

9

2.02509.263159.858240.54963.286011.524091

1.33443.36619.380519.38539.387

99.388199.39

1.17412.44105.24008.812314.47327.34543.882

1.10402.08143.93575.99888.904714.65921.139

1.0648

1.89113.31634.77256.681010.15813.772

1.03981.77332.95774.09905.52347.976110.391

1.02241.69312.72473.67674.82326.71888.5138

1.00971.63502.56123.38814.35725.91067.3386

1.00001.59092.44033.17894.02605.35116.5411

.992321.5563

2.34733.02043.77904.94245.9676

.986101.32842.27352.89623.58794.63155.5368

.980971.50542.21352.79643.43584.3875

5.2021

10

2.04199.320260.195241.88968.636055.824224

1.34503.37709.391619.39639.398

99.399199.40

1.18332.44475.23048.785514.41927.22943.686

1.11262.08203.91995.96448.843914.54620.967

1.0730

1.88993.29744.73516.619210.05113.618

1.04781.77082.93694.06005.46137.874110.250

1.03041.68982.70253.63654.76116.62018.3803

1.01751.63102.53803.34724.29515.81437.2107

100771.58632.41633.13733.96395.25656.4171

1.00001.5513

2.32262.97823.71684.84925.8467

.993731.52302.24822.85363.52574.53935.4182

.988561.49962.18782.75343.37364.2961

5.0855

11

2.05589.367260.473242.99973.046083.324334

1.35373.38599.400619.40539.407

99.408199.41

1.19092.44765.22238.763214.37427.13243.523

1.11962.08233.90665.93578.793314.45220.824

1.0798

1.89873.28154.70386.56769.962313.490

1.05451.76862.91934.02725.40947.789110.132

1.03691.68682.68373.60284.70916.53778.2691

1.02391.62742.51843.31274.24315.73387.1039

1.01411.58222.39593.10223.91175.17746.3136

1.00631.5468

2.30162.94263.66454.77105.7456

.999991.51812.22672.81763.47334.46195.3190

.994801.49452.16582.71703.32114.2193

4.9888

12

2.059.4060.7243.976.6106244

1.363.399.4019.439.4

99.4199.

1.192.455.218.7414.327.043.3

1.122.083.895.91

8.75114.520.7

1.08

1.883.264.676.529.8813.3

1.06l.762.903.995.367.7110.0

1.041.682.663.574.666.468.17

1.021.622.503.284.195.667.01

1.011.572.373.073.865.116.22

1.011.54

2.282.913.624.705.66

1.001.512.202.783.424.395.23

1.001.492.142.683.274.15

4.90

Valores Percentiles , , de la Distribución F. (ContinuaciónPág. 6


13/17

.500

.750

.90013 .950

.975

.990

.995

.500

.750

.90014 .950

.975

.990.995

.500

.750

.90015 .950

.975

.990

.995

.500

.750

.90016 .950

.975

.990

.995

.500

.750.90017 .950

.975

.990

.995

.500

.750

.90018 .950

.975

.990

.995

.500

.750

.90019 .950

.975

.990

.995

.500

.750

.90020 .950

.975

.990

.995

.500

.750

.90021 .950

.975

.990

.995

.500

.750

.90022 .950

.975

.990

.995

.500

.750

.90023 .950

.975

.990

.995

.500

.750

.90024 .950

.975

.990

.995

1

.481411.45003.13624.66726.41439.073811.374

.4 79441.44033.10224.60016.2979

8.861611.060

.477751.43213.07324.54316.19958.683110.798

.476281.42493.04814.49406.11518.531010.575

.4799

1.43863.02624.45136.04208.399710.384

.473851.41303.00704.41395.97818.285410.218

.472841.40812.98994.38085.92168.185010.073

.471921.40372.97474.35133.87158.09609.9439

.471081.39972.96094.32485.82668.01669.8295

.470331.3961

2.94864.30095.78637.94549.7271

.469651.39282.93744.27935.74987.88119.6348

.469021.38982.92714.25975.71677.8229

9.5513

2

.731451.54522.76323.80564.96536.70108.1865

.728621.53312.72653.73894.8567

6.51497.9216

.726191.52272.69523.68234.76506.35897.7008

.724061.51372.66823.63374.68676.22627.5138

.72219

1.50572.64463.59154.61896.11217.3536

.720531.49882.62393.55974.55976.01297.2148

.719061.49252.60563.52194.50755.92597.0935

.717731.48702.58933.49284.46135.84896.9865

.716531.48202.57463.46684.41995.78046.8914

.715451.4774

2.56133.44344.38285.71906.8064

.714461.47332.54933.42214.34925.66376.7300

.713561.46952.53833.40284.31875.6136

6.6609

3

.831591.54512.56033.41054.34725.73946.9257

.828421.53172.52223.34394.2417

5.56396.6803

.825691.52022.48983.28744.15285.41706.4760

.823301.51032.46183.23894.07685.29226.3034

.82121

1.50152.43743.19684.01125.18506.1556

.819361.49382.41603.15993.95395.09196.0277

.817711.48702.39703.12743.90345.01035.9161

.816211.48082.38013.09843.85874.93825.8177

.814871.47532.36493.07253.81884.87405.7304

.613651.4703

2.35123.04913.78294.81665.6524

.812551.46572.33873.02803.75054.76495.5823

.811531.46152.32743.00883.72114.7181

5.5190

4

.884541.53362.43373.17913.99595.20536.2335

.881191.51942.39473.11223.8919

5.03345.9984

.878301.50712.36143.05563.80434.89325.8029

.875781.49652.33273.00693.72944.77265.6378

.87357

1.48732.30772.96473.66484.66905.4967

.871611.47902.28582.92773.60834.57905.3746

.869871.47172.26632.89513.55874.50035.2681

.868301.46522.24892.86613.51474.43075.1743

.866881.45932.23332.84013.47544.36885.0911

.865591.4540

2.21932.81673.44014.31345.0168

.864421.44912.20652.79553.40834.26354.9500

.863351.44472.19492.77633.31944.2184

4.8898

5

.917181.52142.34673.02543.76674.86165.7910

.913711.50662.30692.95823.6634

4.69505.5623

.910731.49382.27302.90133.57644.55565.3721

.908121.48272.24382.85243.50214.43745.2117

.90584

1.47302.21032.81003.43794.33595.0746

.903811.46442.19582.77293.38204.24794.9560

.902001.45682.17602.74013.33274.17084.8526

.900381.45002.15822.71093.28914.10274.7616

.898911.44382.14232.68483.25014.04214.6808

.897591.4382

2.12792.66133.21523.98804.6088

.896381.43312.11492.64003.18353.93924.5441

.895271.42852.10302.62073.15483.8951

4.4857

6

.939261.51052.28302.91533.60434.62045.4819

.935731.49522.24262.84773.5014

4.45585.2574

.932671.48202.20812.79053.41474.31835.0708

.930011.47052.17832.74133.34064.20164.9134

.92767

1.46052.15242.69873.27674.10154.7789

.925601.45162.12962.66133.22094.01464.6627

.923751.44372.10942.62833.17183.93864.5614

.922101.43662.09132.59903.12833.87144.4721

.920601.43022.07512.57273.08953.81174.3931

.919241.4244

2.06052.54913.05463.75834.3225

.918001.41912.04722.52773.02323.71024.2591

.916871.41432.03512.50822.99463.6667

4.2019

7

.9.55201.50112.23412.83213.48274.44105.2529

.951611.48542.19312.76423.3799

4.27795.0313

.948501.47182.15822.70663.29344.14154.8473

.945801.46012.12802.65723.21944.02594.6920

.94342

1.44972.10172.61433.15563.92674.5594

.941321.44062.07852.57673.09993.84064.4448

.939441.43252.05802.54353.05093.76534.3448

.937761.42522.03972.51403.00743.69874.2569

.936241.41862.02322.48762.96863.63964.1789

.934861.4126

2.00842.46382.93383.58674.1094

.933601.40721.99492.44222.90243.53904.0469

.932451.40221.98262.42262.87383.4959

3.9905

8

.967241.49312.19532.76693.38804.30215.0761

.963601.47702.15392.69873.2853

4.13994.8566

.960461.46312.11852.64083.19874.00454.6743

.957731.45112.08802.59113.12483.88964.5207

.95532

1.44052.06132.54803.06103.79104.3893

.953191.43122.03792.51023.00533.70544.2759

.951291.42282.01712.47682.95633.63054.1770

.949591.41531.99852.44712.91283.56444.0900

.948051.40861.98192.42052.87403.30564.0128

.946651.4025

1.96682.39652.83925.45303.9440

.945381.39691.95312.37482.80773.40573.8822

.944221.39181.94072.35512.77913.3629

3.8264

9

.976651.48612.16382.71443.31204.19114.9351

.972981.46972.12202.64583.2093

4.02974.7173

.969811.45562.08622.58763.12273.89484.5364

.967051.44332.05532.53773.04883.78044.3838

.96462

1.43252.02842.49432.98493.68224.2535

.962471.42302.00472.45632.92913.5971

4.1410

.960561.41451.98362.42272.88003.52254.0428

.958841.40691.96492.39282.83653.45673.9564

.957281.40001.94802.36612.79773.39813.9799

.955881.3937

1.93272.34192.76283.34583.8116

.954591.38801.91892.32012.73133.29863.7502

.953421.38261.90632.30022.70273.2560

3.6949

10

.984211.48012.13762.67103.24974.10034.8199

.980511.46342.09542.60213.1469

3.93944.6034

.977321.44912.05932.54373.06023.80494.4236

.974541.43662.02812.49352.98623.69094.2719

.97209

1.42562.00092.44992.92223.59314.1423

.96993l.4159

1.97702.41172.86643.50824.0305

.968001.40731.95572.37792.81733.43383.9329

.966261.39951.93672.34792.77373.36823.8470

.964701.39251.91972.32102.73483.30983.7709

.963281.3861

1.90432.29672.69983.25763.7030

.961991.38031.89032.27472.66823.21063.6420

.960811.37501.87752.25472.63963.1681

3.5870

11

.990421.47462.11522.63433.19714.02394.7234

.986701.45772.07272.56513.0941

3.86344.5078

.983491.44322.03632.50643.00733.72924.3288

.980691.43092.00482.45602.93323.61554.1778

.97823

1.41941.97732.41222.86913.51794.0488

.976061.40951.95322.37372.81323.43313.9374

.974111.40081.93172.35982.76403.35893.8403

.972371.39281.91252.30962.72033.29343.7548

.970791.38571.89532.28252.68133.23513.6790

.969371.3792

1.87982.25802.64633.18303.6114

.968071.37331.86562.23592.61463.13613.5506

.966881.36801.85262.21582.58593.0936

3.4959

1

.9951.472.092.603.153.964.64

.9911.452.052.533.05

3.804.42

.9881.432.012.472.963.664.24

.9851.421.982.422.853.554.09

.983

1.411.952.382.823.453.97

.9811.401.932.342.763.373.85

.9791.391.912.302.713.293.76

.9771.381.892.272.673.233.67

.9751.381.872.252.633.173.60

.9741.37

1.852.222.603.123.53

.9731.361.842.202.563.073.47

.9711.361.832.182.543.03

3.41

Valores Percentiles , de la Distribución F. (Continuación) Pág.


14/17

.500

.750

.90025 .950

.975

.990

.995

.500

.750

.90026 .950

.975

.990.995

.500

.750

.90027 .950

.975

.990

.995

.500

.750

.90028 .950

.975

.990

.995

.500

.750.90029 .950

.975

.990

.995

.500

.750

.90030 .950

.975

.990

.995

.500

.750

.90040 .950

.975

.990

.995

.500

.750

.90048 .950

.975

.990

.995

.500

.750

.90060 .950

.975

.990

.995

.500

.750

.90080 .950

.975

.990

.995

.500

.750

.900120 .950

.975

.990

.995

.500

.750

.900∞ .950

.975

.990

.995

1

.468441.38702,91774.24175.68647.76989.4753

.467931.38452.90914.22525.6586

7.72139.4059

.467441.38222.90124.21005.63317.67679.3423

.466971.38002.89394.19605.60967.63369.2838

.46654

1.37802.86714.18305.58787.39769.2297

.466161.37612.88074.17095.56757.56259.1797

.463301.36262.83544.08485.42397.31418.8278

.461921.35602.81344.04305.35487.19568.6612

.460531.34932.79144.00125.28577.07718.4946

.459141.3428

2.76963.96075.21916.964l8.3368

.457741.33622.74783.92013.15246.85108.1790

.454941.32332.70553.84155.02396.6349

7.8794

2

.712721.46612.52833.38524.29095.56806.5982

.711951.46292.51913.36904.2655

5.52636.5409

.711241.46002.51063.35414.24215.48816.4885

.710591.45732.50283.34044.22055.45296.4403

.70999

1.45472.49953.32774.20065.42056.3958

.709411.45242.48873.31584.18215.39036.3547

.705311.43552.44043.23174.05105.17856.0664

.703271.42727.41683.19113.98825.07805.9307

.701221.41882.39333.15043.92534.97745.7950

.699201.4106

2.37033.11113.86504.88205.6672

.697171.40242.34733.07183.80464.78655.5393

.693131.38632.30262.99573.68894.6052

5.2983

3

.810611.45772.31702.99123.69434.67555.4615

.809751.45422.30752.97513.6697

4.63665.4091

.808941.45102.29872.96043.64724.60095.3611

.808201.44802.29062.94673.62644.56815.3170

.80733

1.44522.28312.93403.60724.53785.2764

.806891.44262.27612.92233.58944.50975.2388

.802281 .42392.22612.83873.46334.31264.9759

.799991.41472.20182.79843.40294.21934.8525

.797701.40552.17742.75813.34254.12594.7290

.795421.3964

2.15372.71923.28484.03754.6132

.793141.38732.13002.68023.22703.94914.4973

.788661.36942.08382.60493.11613.7816

4.2794

4

.862361.44062.18432.75873.35304.17744.8351

.861451.43682.17452.74263.3289

4.14004.7852

.860611.43342.16552.72783.30674.10564.7396

.859831.43022.15712.71413.28634.07404.6977

.85911

1.42722.14942.70143.26744.04494.6591

.858441.42442.14222.68963.24994.01794.6233

.853571.40452.09092.60603.12613.82834.3738

.851151.39472.06602.56563.06693.73874.2569

.848731.38482.04102.52523.00773.64914.1399

.846331.3751

2.01672.48622.95103.56444.0303

.843921.36541.99232.44722.89433.47963.9207

.839181.34631.94492.37192.78583.3192

3.7151

5

.894251.42422.09222.60303.12873.85504.4327

.893311.42032.08222.58683.1048

3.81834.3844

.892441.41662.07302.57193.08283.78484.3402

.891641.41332.06452.55813.06253.75394.2996

.89089

1.41022.05662.54543.04383.72544.2622

.890191.40732.04922.53363.02653.69904.2276

.085161.38631.99602.44952.90373.51383.9860

.882671.37601.97132.40892.84503.42643.8730

.880171.36571.94572.36832.78633.33893.7600

.877691.3555

1.92082.32922.73023.25623.6541

.875211.34531.89592.29002.67403.17353.5482

.870291.32511.84732.21412.56633.0173

3.3499

6

.915831.40992.02412.49042.96853.62724.1500

.914871.40582.01392.47412.9447

3.59114.1027

.913991.40212.00452.45912.92283.55804.0594

.913171.39861.99592.44532.90273.52764.0197

.91741

1.39531.98782.43242.88403.49953.9830

.911691.3923l.98032.42052.86673.47353.9492

.906541.37061.92692.33592.74443.29103.7129

.903991.35991.90082.29502.68593.20493.6024

.901441.34911.87472.25402.62743.11873.4918

.898911.3385

1.84932.21452.57143.03733.3884

.896371.32781.82382.17502.51542.95593.2849

.891351.30681.77412.09862.40822.8020

3.0913

7

.931401.39761.97142.40472.84783.45683.9394

.930421.39351.96102.38832.8240

3.42103.8928

.929521.38961.95152.37322.80213.30823.8501

.928691.38601.94272.35932.78203.35813.8110

.92791

1.38261.93452.34632.76333.33023.7749

.927191.37951.92692.33432.74603.30453.7416

.921971.35711.87252.24902.62383.12383.5088

.919381.34601.84602.20782.56533.03843.4000

.916791.33491.81942.16652.50682.95303.2911

.914221.3239

1.79352.12662.45082.87243.1893

.911641.31281.76752.08672.39482.79183.0874

.906541.29101.71672.00962.28752.6393

2.8968

8

.943151.38711.92922.33712.75313.32393.7758

.942171.38281.91882.32052.7293

3.28843.7797

.941261.37881.90912.30532.70743.25583.6875

.940411.37521.90012.29132.68723.22593.6487

.93963

1.37171.89182.27822.66863.19823.6130

.938891.36851.88412.26622.65133.172635801

.933611.34551.82892.18022.52892.99303.3498

.931001.33411.80192.13862.47032.90823.2421

.928381.32261.77482.09702.41172.82333.1344

.925781.3113

1.74842.05672.35562.74313.0337

.923181.29991.72202.01642.29942.66292.9330

.918021.27741.67021.93842.19182.5113

2.7444

9

.952341.37801.89472.28212.67663.21723.6447

.951351.37371.88412.26552.6528

3.18183.5989

.950441.36961.87432.25012.63093.14943.5571

.949581.36581.86522.23602.61063.11953.5186

.94879

1.36231.85682.22292.59193.09203.4832

.948051.35901.84902.21072.57463.06653.4503

.942721.33541.79292.12402.45192.88763.2270

.940081.32371.76552.08212.39322.80313.1132

.937431.31191.73802.04012.33442.71853.0083

.934811.3003

1.71121.99952.27812.63862.9083

.932181.28861.68431.95882.22172.55862.8083

.926981.26541.63151.87992.11362.4073

2.6210

10

.959721.37011.86582.23652.61353.12943.5370

.958721.36561.85502.21972.5895

3.09413.4916

.957791.36151.84512.20432.56763.06183.4499

.956941.35761.83592.19002.54733.03203.4117

.95614

1.35411.82742.17682.52863.00453.3765

.955401.35071.81952.16462.51122.97913.3440

.950031.32661.76272.07722.38622.80053.1167

.947371.31461.73492.03492.32922.71623.0105

.944711.30261.70701.99262.27022.63182.9042

.942071.2907

1.67971.95162.21362.55202.8047

.939431.27871.65241.91052.15702.47212.7052

.934181.25491.59871.83072.04832.3209

2.5188

11

.965791.36301.84092.19742.55973.05513.4461

.964781.35841.82992.18052.5357

3.01983.4008

.963851.35421.81992.16502.51372.98753.3594

.962981.35021.81062.15072.49342.95783.3213

.96218

1.34681.80202.13742.47452.93033.2863

.961441.34321.79402.12512.45712.90493.2538

.956041.31861.73652.03702.33372.72653.0275

.953361.30631.70821.99432.27442.64212.9216

.950681.29411.67991.95162.21512.55787.8157

.948031.2819

1.65221.91012.15822.47792.7164

.949371.26961.62451.86862.10132.39802.6172

.940101.24521.56981.78791.99182.2467

2.4313

1

.9701.351.822.162.512.993.37

.9691.351.802.142.49

2.953.32

.9681.341.792.132.462.923.28

.9681.342.782.112.442.893.24

.967

1.341.782.102.422.863.21

.9661.331.772.092.412.843.17

.961l.31l.712.002.282.662.95

.9581.291.681.962.222.582,84

.9551.281.651.912.162.492.74

.9521.27

1.621.872.112.412.64

.9501.261.601.832.052.332.54

.9451.231.541.751.942.18

2.35

Valores Percentiles , de la Distribución F. (ContinuaciónPág. 8


15/17

.500

.750

.9001 .950

.975

.990

.995

.500

.750

.9002 .950

.975

.990

.995

.500

.750

.9003 .950

.975

.990

.995

.500

.750

.9004 .950

.975

.990

.995

.500

.750.9005 .950

.975

.990

.995

.500

.750

.9006 .950

.975

.990

.995

.500

.750

.9007 .950

.975

.990.995

.500

.750

.9008 .950

.975

.990

.995

.500

.750

.9009 .950

.975

.990

.995

.500

.750

.90010 .950

.975

.990

.995

.500

.750

.90011 .950

.975

.990

.995

.500

.750

.90012 .950

.975

.990

.995

13

2.07739.439960.903244.69979.856123.924504

1.36723.39979.414519.41939.421

99.422199.42

1.20252.45205.20978.728614.30526.98343.271

1.13052.08273.85535.89108.714814.30620.602

1.0903

1.88673.25664.65506.48739.824413.292

1.06471.76502.89183.97615.32877.65709.9494

1.04691.68192.65433.55014.62816.40968.0962

1.003391.62162.48753.25884.16185.60856.9377

1.02391.57562.36383.04723.83025.05406.1524

1.01611.5395

2.26852.88683.58274.64915.5880

1.00971.51022.19272.76113.39134.34115.1642

1.00441.48612.13112.65983.23884.0993

4.8352

14

2.08589.468561.073245.37982.546142.724572

1.37253.40519.420019.42439.426

99.427199.43

1.20712.45375.20478.714814.27726.92343.171

1.13492.08283.87655.87328.683614.24820.514

1.0944

1.88583.24664.63566.45549.769713.214

1.06871.76342.88083.95585.29667.60459.8769

1.05091.67992.64253.52914.59586.35858.0274

1.03781.61912.47503.23714.12935.55846.8716

1.02781.57292.35083.02523.79765.00486.0882

1.01991.5364

2.25512.86443.55004.60045.5252

1.01351.50692.17902.73833.35844.29285.1024

1.00821.48262.11702.63583.20384.0512

4.7742

15

2.09319.493461.220245.95984.876157.324630

1.37713.40989.424719.42939.431

99.432199.43

1.21112.45525.20038.702914.25326.87243.085

1.13862.08293.86895.85788.656514.19820.438

1.0980

1.88513.23804.61886.4277

9.7222.13.146

1.07221.76212.87123.93813.26877.55909.8140

1.05431.67812.63223.51084.56786.31437.9678

1.04121.61702.46423.21844.10125.51516.8143

1.03111.57052.33963.00613.76944.96216.0325

1.02321.5338

2.24352.84503.52174.55825.4707

1.01681.50412.16712.71863.32994.25095.0489

1.01151.47962.10492.61693.17724.0096

4.7214

18

2.11049.552061.567247.32990.366191.624767

1.38793.42089.435819.44039.442

99.443199.44

1.22052.45855.18988.674414.19626.75147.880

1.14732.08283.85255.82098.592114.07920.257

1.1064

1.88303.21714.57836.36169.609212.984

1.08041.75862.84793.89555.20187.45029.6639

1.06241.67352.60723.46664.50046.20047.8253

1.04911.61152.43783.17304.03345.41116.6769

1.03901.56422.31212.95973.70114.85945.8987

1.03101.5269

2.21502.79773.45304.45635.3396

1.02451.49672.13772.67053.26074.14964.9198

1.01921.47172.07482.56803.10763.9088

4.5937

20

2.11909.581361.740248.01993.106208.724836

1.39933.42639.441319.44639.448

99.449199.45

1.22522.46025.18458.660214.16726.69042.778

1.15172.08283.84435.80258.559914.02020.167

1.1106

1.88203.20674.55816.32859.552712.903

1.08451.75692.83633.87425.16847.39389.5888

1.06641.67122.59473.44454.46676.15547.7540

1.05311.60882.42463.15033.99955.35916.6082

1.04291.56112.29832.93653.66694.80805.8318

1.03491.5235

2.20072.77403.41864.40545.2740

1.02841.49302.12302.64643.22614.09904.8352

1.02311.46782.05972.54363.07283.8584

4.5299

24

2.13219.625562.002249.05997.256234.624940

1.40143.43659.649619.45439.456

99.458199.46

1.23222.46265.17648.638514.12426.59842.622

1.15832.08273.83105.77448.510913.92920.030

1.1170

1.88023.19054.52726.27809.466512.780

1.09071.75402.81833.84155.11727.31279.4741

1.07241.66752.57533.41054.41506.07437.6450

1.05911.60432.40413.11523.94725.27936.5029

1.04891.55602.27682.90053.61424.72905.7292

1.04081.5179

2.17842.73723.36544.32695.1732

1.03431.48692.10002.60903.17254.02094.7557

1.02891.46132.03602.50553.01873.7805

4.4315

30

2.14529.669862.265250.091001.46260.725044

1.40963.44289.457919.46239.465

99.466199.47

1.23932.46505.16818.616614.08126.50542.466

1.16492.08253.81745.74598.461313.83819.892

1.1234

1.87843.17414.49576.22699.379312.656

1.09691.75102.80003.80825.06527.22859.3583

1.07851.66352.55553.37584.36245.99217.5345

1.06511.59962.38303.07943.89405.19816.3961

1.05481.55062.25472.86373.56044.64865.6248

1.04671.5119

2.15542.69963.31104.24695.0705

1.04011.48052.07622.57053.11763.94114.0543

1.03471.45442.01152.46632.96333.7008

4.3309

40

2.15849.714462.529

251. 141005.66286.825148

1.41783.45119.466219.47139.473

99.474199.47

1.24642.46745.15978.594414.037

26.41 142.308

1.17162.08213.80365.71708.411113.74519.752

1.1297

1.87633.15734.46386.17519.291212.530

1.10311.74772.78123.77435.01257.14329.2408

1.08461.65932.53513.34044.30895.90847.4225

1.07111.59452.36143.04283.83985.11366.2875

1.06081.54502.23202.82593.50554.56675.5186

1.05261.5056

2.13172.66093.25544.16534.9659

1.04601.47372.05162.53093.06133.85964.5508

1.04051.44711.98612.42592.90633.6192

4.2282

48

2.16509.736862.662251.671007.76299.925201

1.42203.45539.470519.47539.477

99.478199.47

1.25002.46865.15558.583214.01526.36442.229

1.17492.08193.79665.70248.385813.69919.682

1.1329

1.87533.14884.44766.14889.246612.466

1.10621.74602.77163.75714.98577.10009.1814

1.08771.65712.52473.32244.28175.86607.3657

1.07411.59192.35033.02413.81215.07366.2324

1.06381.54202.22032.80663.47744.52495.4645

1.05561.5023

2.11952.64103.22694.12364.9126

1.04901.47012.03892.51053.03243.81794.4979

1.04351.44321.97292.40512.87713.5774

4.1756

60

2.17169.759162.794252.201009.86313.025253

1.42613.45949.474619.47939.481

99.483199.48

1.25362.46975.15128.572013.99226.31642.149

1.17822.08173.78965.68788.360413.65219.611

1.1361

1.87423.14024.43146.12259.202012.402

1.10931.74432.76203.73984.95897.05689.1219

1.09081.65482.51423.30434.25445.82367.3088

1.07711.56922.33913.00533.78445.03166.1772

1.06671.53892.20852.78723.44934.48315.4104

1.05851.4990

2.10722.62113.19844.08194.8592

1.05191.46642.02612.49013.00353.77614.4450

1.04641.43931.95972.38422.84783.5355

4.1229

120

2.18489.804163.061253.251014.06339.425359

1.43443.46779.482919.48739.490

99.491199.49

1.26082.47205.14258.549413.94726.22141.989

1.18492.08123.77535.65818.309213.55819.468

1.1426

1.87193.12284.39846.06939.111812.274

1.11561.74072.74233.70474.90456.96909.0015

1.09691.65022.49283.26744.19895.73727.1933

1.08321.58362.31622.96693.72794.94606.0649

1.07271.53252.18432.74753.39184.39785.3001

1.06451.4919

2.08182.58013.13993.99654.7501

1.05781.45871.99972.44802.94413.69044.3367

1.05231.43101.93232.34102.78743.4494

4.0149

∞

2.199.8463.3254.10186366224

1.443.479.4919.439.4

99.4199.

1.262.475.138.5213.926.141.8

1.192.083.765.628.2513.419.3

1.14

1.863.104.366.019.0212.1

1.121.732.723.664.846.858.87

1.101.642.473.224.145.647.07

1.081.572.292.923.674.855.95

1.071.522.152.703.334.315.18

1.071.48

2.052.533.073.904.63

1.061.451.972.402.883.604.22

1.05l.421.902.292.723.36

3.90

Valores Percentiles , de la Distribución F. (Continuación) Pág.


16/17

.500

.750

.90013 .950

.975

.990

.995

.500

.750

.90014 .950

.975

.990.995

.500

.750

.90015 .950

.975

.990

.995

.500

.750

.90016 .950

.975

.990

.995

.500

.750.90017 .950

.975

.990

.995

.500

.750

.90018 .950

.975

.990

.995

.500

.750

.90019 .950

.975

.990

.995

.500

.750

.90020 .950

.975

.990

.995

.500

.750

.90021 .950

.975

.990

.995

.500

.750

.90022 .950

.975

.990

.995

.500

.750

.90023 .950

.975

.990

.995

.500

.750

.90024 .950

.975

.990

.995

13

1.00001.46582.07992.57653.11453.90464.5726

.996261.44852.03672.50633.0113

3.74464.3584

.993001.43371.99982.44772.92443.61084.1806

.990181.42071.96792.39682.85003.45004.0306

.98769

1.40931.94002.35262.78573.40003.9024

.985501.39921.91542.31382.72963.31533.7917

.953541.39011.89362.27962.66023.24143.6952

.981781.38201.87412.24902.63633.17613.6102

.980191.37471.85662.22172.59723.11793.5349

.978751.3680

1.84082.19702.56203.06593.4677

.977441.36201.82632.17462.53013.01903.4073

.976241.35641.81312.15432.50132.9766

3.3529

14

1.00381.46222.06562.55833.08143.85684.5123

1.00001.44472.02212.48332.9781

3.69704.2986

.996751.42971.98502.42402.89103.56334.1212

.993921.41661.95292.37292.81653.45003.9716

.99143

1.40511.92482.32862.75213.35273.8438

.989221.39481.90012.28962.69593.26823.7333

.987251.38571.87812.25522.64643.19423.6370

.985491.37751.85852.22452.60243.12893.5523

.983891.37011.64092.19702.56323.07083.4771

.982451.3634

1.82492.17222.52793.01883.4100

.981131.35721.81032.14972.49602.97193.3498

.979931.35161.79702.12932.46712.9295

3.2954

15

1.00711.45902.05322.53313.05273.81544.4600

1.00331.44142.00952.46302.9493

3.65574.2468

1.00001.42631.97222.40332.86233.52224.0698

.997161.41301.93992.35222.78753.40893.9205

.99466

1.40141.91172.30772.72303.31173.7929

.992451.39111.88682.26862.66673.22733.6827

.990471.38191.86472.23412.61713.15933.5866

.988701.37361.54492.20332.57313.08803.5020

.987101.36611.82722.17572.53383.02993.4270

.985651.3593

1.81112.35082.49842.97803.3600

.984331.35311.79642.12822.46652.93113.2999

.983121.34741.70312.10772.43742.8887

3.2456

18

1.01481.45072.02242.48362.98273.71494.3333

1.01091.43271.97822.41292.8789

3.55544.1213

1.00761.41721.94032.35282.79133.42203.9450

1.00481.40371.90752.30112.71643.30883.7963

1.0022

1.39171.87882.25622.65153.21163.6692

1.00001.38121.85332.21662.59493.12723.5594

.998021.97171.83102.18172.54503.05323.4633

.996231.36321.81082.15062.50072.98783.3792

.994621.35551.79282.12262.46112.92973.3044

.993161.3485

1.77642.09742.42552.87763.2376

.991831.34221.76142.07452.39332.83073.1776

.990611.33631.74782.05372.36402.7882

3.1235

20

1.01861.44652.00702.45892.94773.66464.2703

1.01471.42841.96252.38792.8437

3.50524.0585

1.01141.41271.92432.32752.75593.97893.8826

1.00861.39901.89132.27562.68083.25883.7342

1.0060

1.38691.86242.23042.61583.16153.6073

1.00381.37621.83682.19062.55903.07713.4977

1.00181.36661.81422.15552.50893.00313.4020

1.00001.35801.79382.12422.46452.93773.3178

.998381.35021.77562.09602.42472.87963.2431

.996921.3431

1.75902.07072.38902.82743.1764

.995581.33661.74392.04762.35672.78053.1165

.994361.33071.73022.02672.32732.7380

3.0624

24

1.02431.43971.98272.42022.89323.58684.1726

1.02051.42121.93772.34872.7888

3.42743.9614

1.17201.40521.89902.26782.70063.29403.7859

1.01431.39131.86562.23542.62523.18083.6378

1.0117

1.37901.63622.18982.55983.08353.5112

1.00951.36801.81032.14972.50272.99903.4017

1.00751.35821.78732.11412.45232.92493.3062

1.00571.34941.76672.08252.40762.85943.2220

1.00401.34141.74812.05402.36752.80113.1474

1.00261.3341

1.73122.02832.33152.74883.0807

1.00121.32751.71592.00502.29892.70173.0208

1.00001.32141.70191.98382.26932.6591

2.9667

30

1.03011.49241.95762.38032.83733.50704.0727

1.02631.41361.91192.30822.7324

3.34763.8619

1.02291.39731.87282.24682.64373.21413.6867

1.02001.36301.83882.19382.56783.10073.5388

1.0174

1.37041.80902.14772.50213.00323.4124

1.01521.35921.78272.10712.44452.91853.3030

1.01321.34921.75922.07122.39372.84423.2075

1.01141.34011.73822.03912.34862.77853.1234

1.00971.33191.71932.01022.30822.72003.0488

1.00821.3245

1.70211.98422.27182.66752.9821

1.00691.31761.68641.96052.23892.62022.9221

1.00571.31131.67211.93902.20902.5773

2.8679

40

1.03601.42471.93152.33972.77973.42533.9704

1.03211.40551.88522.26642.6747

3.26563.7600

1.02871.38881.84542.20652.58503.13193.5850

1.02581.37421.81082.15072.50853.01823.4372

1.0232

1.36131.78052.10402.44222.92053.3107

1.02091.34971.75372.06292.38422.83543.2014

1.01891.33941.72982.02642.33292.76083.1058

1.01711.33011.70831.99382.28732.69473.0215

1.01541.32171.68901.96452.24652.63592.9467

1.01391.3140

1.67141.93802.20972.58312.8799

1.01261.30691.65541.91392.17632.53552.8198

1.01131.30041.64071.89202.14602.4923

2.7654

48

1.03891.42061.91792.91792.75013.38333.9180

1.03501.40111.87122.24472.6442

3.22353.7077

1.03161.38471.83112.10222.55463.08953.5327

1.02871.36941.79622.12832.47782.97563.3848

1.0261

1.35641.76562.08122.41122.87773.2483

1.02381.34461.73852.03982.35282.79243.1488

1.02181.33421.71432.00302.30122.71733.0531

1.02001.32471.69261.97012.25542.65122.9687

1.01831.31611.67301.94952.21422.59222.8938

1.01681.3083

1.65521.91382.17722.53912.8268

1.01551.30111.63891.88942.14352.49132.7665

1.01421.29451.62401.86722.11302.4479

2.7120

60

1.04181.41641.90432.29662.72043.34133.8655

1.03791.39671.85722.22302.6142

3.18133.6553

1.03451.37961.81682.16012.52423.04713.4803

1.03151.36461.78162.10582.44712.93303.3324

1.0289

1.35141.75062.05842.38012.83483.2058

1.02671.33951.72322.01662.32142.74933.0962

1.02461.32891.69881.97962.26932.67423.0004

1.02281.31931.67681.94642.22342.60772.9159

1.02111.31051.65691.91652.18192.54842.8408

1.01961.3025

1.63891.88952.14462.49512.7736

1.01831.29521.62241.86492.11072.44712.7132

1.01701.28851.60731.84242.07992.4035

2.6585

120

1.04761.40751.87592.25242.69903.23483.7577

1.04371.38741.82802.37782.5519

3.09423.5473

1.04031.36981.78672.11412.46112.95053.3722

1.03731.35431.75072.05892.38312.84473.7240

1.0347

1.34061.71912.01072.31572.74593.0971

1.03241.32841.69101.96812.25582.65972.9871

1.03041.31741.66591.93022.20322.58392.8908

1.02851.30741.64331.89632.15622.51682.8058

1.02681.29831.62281.86572.11412.45682.7302

1.02531.2900

1.60421.83802.07602.40292.6625

1.02401.28241.58711.81282.04152.35422.6016

1.02271.27541.57151.78972.00992.3099

2.5463

∞

1.091.391.842.202.593.163.84

1.041.371.792.132.48

3.003.43

1.041.351.752.062.392.863.26

1.041.341.712.002.312.753.11

1.04

1.321.641.962.242.652.98

1.031.321.651.912.182.562.87

1.031.301.631.872.132.482.77

1.031.291.601.842.082.422.69

1.031.281.581.812.042.362.61

1.031.27

1.561.782.002.302.54

1.021.261.541.751.962.252.48

1.021.261.531.731.932.21

2.42

Valores Percentiles , de la Distribución F. (Continuación)Pág. 10


17/17

.500

.750

.90025 .950

.975

.990

.995

.500

.750

.90026 .950

.975

.990.995

.500

.750

.90027 .950

.975

.990

.995

.500

.750

.90028 .950

.975

.990

.995

.500

.750.90029 .950

.975

.990

.995

.500

.750

.90030 .950

.975

.990

.995

.500

.750

.90040 .950

.975

.990

.995

.500

.750

.90048 .950

.975

.990

.995

.500

.750

.90060 .950

.975

.990

.995

.500

.750

.90080 .950

.975

.990

.995

.500

.750

.900120 .950

.975

.990

.995

.500

.750

.900∞ .950

.975990

13

.975141.35131.80112.13572.47492.93813.3034

.974121.34661.79002.11862.4508

2.90293.2584

.973181.34231.77982.10292.42862.87063.2172

.972311.33821.77032.08842.40822.84093.1793

.97180

1.33441.76152.07492.38922.81353.1445

.970751.33091.75332.06242.37172.78813.1122

.965301.30551.69451.97312.24732.60972.8869

.962601.29281.66561.92972.18752.52932.7815

.959901.28011.63661.88622.12772.44082.6760

.957221.2674

1.60811.84402.07012.36072.5770

.954541.25471.57961.80172.01262.28062.4781

.949221.22911.52321.71921.90162 1285

14

.978821.34641.78492.11062.44072.89103.2460

.977801.34171.77372.09342.4165

2.85583.2011

.976851.33721.76342.07772.39422.82353.1600

.975981.33321.75382.06302.37372.79383.1222

.97517

1.32931.74492.04952.35472.76643.0874

.974411.32581.73672.03692.33712.74103.0551

.968951.30001.67731.94712.21232.56252.8302

.966241.28711.64811.90332.15222.47802.7249

.963521.27421.61881.85952.09212.39342.6195

.960841.7613

1.58991.81692.03432.31312.5205

.958151.24831.56111.77431.

formularios oficiales + tablas estadisticas - alejandro gonzalez (corregidos)

Documents