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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
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(*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
Alejandro González Tapia - Ing. Civil en Minas
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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 ̅∑ ̅
Alejandro González Tapia - Ing. Civil en Minas
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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 ̅∑ ̅
Alejandro González Tapia - Ing. Civil en Minas
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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
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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
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-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
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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
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8/17/2019 Formularios oficiales + Tablas Estadisticas - Alejandro Gonzalez (Corregidos)
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
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8/17/2019 Formularios oficiales + Tablas Estadisticas - Alejandro Gonzalez (Corregidos)
10/17
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11/17
0 . 9
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1
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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
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2.92454.10285.45647.53949.4772
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.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
-
8/17/2019 Formularios oficiales + Tablas Estadisticas - Alejandro Gonzalez (Corregidos)
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.
-
8/17/2019 Formularios oficiales + Tablas Estadisticas - Alejandro Gonzalez (Corregidos)
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
-
8/17/2019 Formularios oficiales + Tablas Estadisticas - Alejandro Gonzalez (Corregidos)
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.
-
8/17/2019 Formularios oficiales + Tablas Estadisticas - Alejandro Gonzalez (Corregidos)
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
-
8/17/2019 Formularios oficiales + Tablas Estadisticas - Alejandro Gonzalez (Corregidos)
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.