I VA -Número 2

26
Cálculos K 7 Máx. 2300 74.83 Mín. 246 417.18 Amplitude 2054 759.53 Amp. Classe 342.35 1101.88 Limite Inferior 74.825 1444.23 1786.58 2128.93 2471.28 2813.63 3155.98 Média 930.70 Variancia 399360.150741 Desvio Padrão 631.95 1.07533592644 Curtose 0.14450936587 Distribuição - - Digitar Valor da Linha Valor da Coluna Linha - - - Probabilidade de Não - Excedência Probabilida - TEMPO DE RETORNO TEMPO - TR - PROBABILIDADE - - Coeficiente de Assimetria XTR KTR KTR X TR MÁX. X TR MÍN.

description

Memorial de Weibul e probabilidade

Transcript of I VA -Número 2

Page 1: I VA -Número 2

Cálculos de Estatística Aplicada à Hidrologia

K 7 PMáx. 2300 74.83 -Mín. 246 417.17 -Amplitude 2054 759.52 -Amp. Classe 342.35 1101.87 -Limite Inferior 74.825 1444.22 -

1786.57 -2128.92 -2471.27 -2813.62 -3155.97 -

Média 930.70Variancia 399360.1507407Desvio Padrão 631.95

1.075335926437

Curtose 0.14450936587

Distribuição Normal (Gauss)

--

DigitarValor da Linha Valor da Coluna Linha Coluna

- - - -

Probabilidade de Não - Excedência Probabilidade de EXCEDÊNCIA- -

TEMPO DE RETORNO TEMPO DE RETORNO- -

TR -PROBABILIDADE -

-

--

Coeficiente de Assimetria

XTR

KTR

KTR

XTR MÁX.

XTR MÍN.

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Calculo de Probabilidade (Z)

0.33267

0.43618

-0.12017

0.9373

Z q F(z) P(z)1.64500 0.6463112448171 0.103110811092 0.9500160721535491.64510 0.6462973488837 0.1030938502431 0.9500263790734361.64520 0.6462834535478 0.1030768911534 0.9500366842973971.64530 0.6462695588094 0.1030599338229 0.950046987825611.64540 0.6462556646684 0.1030429782516 0.950057289658251.64550 0.6462417711248 0.1030260244396 0.9500675897954941.64560 0.6462278781786 0.103009072387 0.9500778882375171.64570 0.6462139858298 0.1029921220937 0.9500881849844971.64580 0.6462000940782 0.1029751735599 0.9500984800366091.64590 0.6461862029239 0.1029582267856 0.9501087733940291.64600 0.6461723123668 0.1029412817708 0.950119065056935

Z Variação (Δ)#VALUE! #VALUE!

a0

a1

a2

a3

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Cálculos de Estatística Aplicada à Hidrologia

P f ῑ f.ῑ (ῑ-x)²f (ῑ-x)³f417.17 10 246.0 2460 4688140.9 -3209970074 2.197867E+12759.52 18 588.3 10590.3 2109663.4 -722243267247259982355

1101.87 12 930.7 11168.4 0 0 01444.22 6 1273.0 7638.3 703221.135 240747756 824199941181786.57 2 1615.4 3230.8 937628.18 6419940154395733019652128.92 0 1957.7 0 0 0 02471.27 7 2300.1 16100.7 13126794.517975832416 2.46161E+132813.62 0 2642.5 0 0 0 03155.97 0 2984.8 0 0 0 03498.32 0 3327.1 0 0 0 0

somatorio 55 51188.5 21565448.1 14926360845 2.758322E+13

Distribuição Normal (Gauss)

Probabilidade de EXCEDÊNCIA-

TEMPO DE RETORNO-

(ῑ-x)4f

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Calculo de Probabilidade (Z)

Variação (Δ) Z#VALUE! 1.645#VALUE! 1.645#VALUE! 1.645#VALUE! 1.645#VALUE! 1.645#VALUE! 1.646#VALUE! 1.646#VALUE! 1.646#VALUE! 1.646#VALUE! 1.646#VALUE! 1.646

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Cálculos de Estatística Aplicada à Hidrologia

LN(ῑ)5.5053326.3773226.8359377.1491717.3873387.5795517.7407087.8794628.0012888.10987172.56598

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Planilha de DadosID Precipitação

1940 9531941 11711942 7231943 2671944 6461945 3651946 13591947 4111948 4801949 3651950 11921951 3561952 2461953 10931954 8401955 6221956 23001957 5981958 6461959 9531960 23001961 7181962 5031963 23001964 4571965 9151966 7421967 8401968 3311969 3201970 3651971 6711972 17851973 7261974 3971975 4801976 23001977 6731978 7601979 7801980 6531981 5371982 9451983 16501984 1165

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1985 8881986 7281987 8091988 9451989 13801990 23001991 23001992 23001993 11151994 63919951996199719981999200020012002200320042005200620072008200920102011201220132014201520162017201820192020202120222023202420252026202720282029203020312032

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2033203420352036203720382039

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Distribuição de Gumbel para Máximos

α 0.00202959260480542 -

μ 646.32273205 TR -TR -

Probabilidade de Não - Excedência

- -

Distribuição de Gumbel para Mínimos

α 0.00202959260480542μ 1215.07726795

-

Probabilidade de Não - Excedência Probabilidade de EXCEDÊNCIA- -

TR -

-

XTR

XTR

XTR

XTR

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Distribuição de Gumbel para Máximos

Probabilidade de Não - Excedência Probabilidade de EXCEDÊNCIA- -

Distribuição de Gumbel para Mínimos

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930.7 631.949484326667 399360.15074074θ

6.9589239

1.00000000019001

76.1800917294714

-86.5053203294167 Digitar TR24.0140982408309 X

-1.23173957245015

0.00120865097386617

Г(n)θ PARCELA Ps1

6.9589239 0.856299621267593 0.712599242535186 2.927279 3.517585 17.72669017976.95892391 0.856299621474091 0.712599242948182 2.927279 3.517585 17.7266901776.95892392 0.856299621680589 0.712599243361178 2.927279 3.517585 17.72669017436.95892393 0.856299621887087 0.712599243774174 2.927279 3.517585 17.72669017166.95892394 0.856299622093585 0.71259924418717 2.927279 3.517585 17.72669016896.95892395 0.856299622300083 0.712599244600165 2.927279 3.517585 17.72669016626.95892396 0.856299622506581 0.712599245013162 2.927279 3.517585 17.72669016356.95892397 0.856299622713079 0.712599245426157 2.927279 3.517585 17.72669016086.95892398 0.856299622919577 0.712599245839154 2.927279 3.517585 17.72669015816.95892399 0.856299623126075 0.712599246252149 2.927279 3.517585 17.72669015546.958924 0.856299623332573 0.712599246665145 2.927279 3.517585 17.72669015276.95892401 0.856299623539071 0.712599247078141 2.927279 3.517585 17.726690156.95892402 0.856299623745569 0.712599247491137 2.927279 3.517585 17.72669014736.95892403 0.856299623952067 0.712599247904133 2.927279 3.517585 17.72669014466.95892404 0.856299624158565 0.712599248317129 2.927279 3.517585 17.72669014196.95892405 0.856299624365063 0.712599248730125 2.927279 3.517585 17.72669013926.95892406 0.856299624571561 0.712599249143121 2.927279 3.517585 17.72669013656.95892407 0.856299624778059 0.712599249556117 2.927279 3.517585 17.72669013386.95892408 0.856299624984557 0.712599249969113 2.927279 3.517585 17.72669013116.95892409 0.856299625191055 0.712599250382109 2.927279 3.517585 17.7266901284

β Δ Г(n)6.9589239 361100.8864 1.10655181763536

Média (μ) Desvio Padrão (σ) Variância (σ²)

P0

P1

P2

P3

P4

P5

N1(1-(1/θ)) N2(1-(2/θ)) √(2π)/N1 √(2π)/N2

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Г(n) λ1.10655181764 841.081262682168

- Digitar X -- TR -

Г(n)PARCELA Ps2 Parcela 1 = e-(N+5,5)

19.7990627557 12.2853001128459 9.16057322228189 0.001735777878214519.7990627492 12.285300118079 9.16057322993079 0.0017357778778560619.7990627426 12.2853001233122 9.16057323757968 0.00173577787749763

19.799062736 12.2853001285454 9.16057324522858 0.0017357778771391919.7990627295 12.2853001337785 9.16057325287748 0.0017357778767807619.7990627229 12.2853001390117 9.16057326052637 0.0017357778764223219.7990627163 12.2853001442448 9.16057326817527 0.0017357778760638919.7990627097 12.285300149478 9.16057327582416 0.0017357778757054619.7990627032 12.2853001547112 9.16057328347306 0.0017357778753470219.7990626966 12.2853001599443 9.16057329112195 0.00173577787498858

19.79906269 12.2853001651775 9.16057329877085 0.0017357778746301519.7990626835 12.2853001704106 9.16057330641975 0.0017357778742717219.7990626769 12.2853001756438 9.16057331406865 0.0017357778739132819.7990626703 12.285300180877 9.16057332171754 0.0017357778735548519.7990626638 12.2853001861101 9.16057332936643 0.0017357778731964119.7990626572 12.2853001913433 9.16057333701533 0.0017357778728379819.7990626506 12.2853001965764 9.16057334466423 0.0017357778724795419.7990626441 12.2853002018096 9.16057335231312 0.0017357778721211119.7990626375 12.2853002070428 9.16057335996202 0.0017357778717626719.7990626309 12.2853002122759 9.16057336761092 0.00173577787140424

Parcela 1 = (N+5,5)N+0,5 Parcela 2 = (N+5,5)N+0,5

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Г(n)Parcela 2 = e-(N+5,5)

0.00200402174997959 1.106552 1.27854 38259.2643306683 361100.8864 6.9589240.00200402174915194 1.106552 1.27854 38259.2642026635 361100.8865 6.9589240.00200402174832429 1.106552 1.27854 38259.2640746613 361100.8867 6.9589240.00200402174749663 1.106552 1.27854 38259.2639466573 361100.8868 6.9589240.00200402174666898 1.106552 1.27854 38259.2638186551 361100.8869 6.9589240.00200402174584133 1.106552 1.27854 38259.2636906512 361100.8871 6.9589240.00200402174501367 1.106552 1.27854 38259.2635626482 361100.8872 6.9589240.00200402174418602 1.106552 1.27854 38259.263434644 361100.8873 6.9589240.00200402174335837 1.106552 1.27854 38259.2633066423 361100.8874 6.9589240.00200402174253072 1.106552 1.27854 38259.2631786389 361100.8876 6.9589240.00200402174170306 1.106552 1.27854 38259.2630506363 361100.8877 6.9589240.00200402174087541 1.106552 1.27854 38259.2629226332 361100.8878 6.9589240.00200402174004776 1.106552 1.27854 38259.2627946285 361100.8879 6.958924

0.0020040217392201 1.106552 1.27854 38259.2626666254 361100.8881 6.9589240.00200402173839245 1.106552 1.27854 38259.2625386221 361100.8882 6.958924

0.0020040217375648 1.106552 1.27854 38259.2624106187 361100.8883 6.9589240.00200402173673715 1.106552 1.27854 38259.262282616 361100.88850.00200402173590949 1.106552 1.27854 38259.2621546123 361100.88860.00200402173508184 1.106552 1.27854 38259.2620266097 361100.88870.00200402173425419 1.106552 1.27854 38259.2618986077 361100.8888

Г(N1) Г(N2) Variância (σ²) Variação (Δ)

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1.1065521.1065521.1065521.1065521.1065521.1065521.1065521.1065521.1065521.1065521.1065521.1065521.1065521.1065521.1065521.1065521.1065521.1065521.1065521.106552

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930.7 631.949484326667 399360.15074074β

1.499914

1.00000000019001

76.1800917294714

-86.5053203294167 TR24.0140982408309 X

-1.23173957245015

0.00120865097386617

Г(n)β PARCELA

1.49991404 1.66670487330061 2.33340974660121 1.503942 1.074234 10.903661.499914041 1.66670487285611 2.33340974571222 1.503942 1.074234 10.903661.499914042 1.66670487241162 2.33340974482323 1.503942 1.074234 10.903661.499914043 1.66670487196712 2.33340974393424 1.503942 1.074234 10.903661.499914044 1.66670487152262 2.33340974304525 1.503942 1.074234 10.903661.499914045 1.66670487107813 2.33340974215626 1.503942 1.074234 10.903661.499914046 1.66670487063363 2.33340974126727 1.503942 1.074234 10.903661.499914047 1.66670487018914 2.33340974037828 1.503942 1.074234 10.903661.499914048 1.66670486974464 2.33340973948929 1.503942 1.074234 10.903661.499914049 1.66670486930015 2.33340973860029 1.503942 1.074234 10.903661.49991405 1.66670486885565 2.3334097377113 1.503942 1.074234 10.903661.499914051 1.66670486841116 2.33340973682231 1.503942 1.074234 10.903661.499914052 1.66670486796666 2.33340973593332 1.503942 1.074234 10.903661.499914053 1.66670486752217 2.33340973504433 1.503942 1.074234 10.903661.499914054 1.66670486707767 2.33340973415534 1.503942 1.074234 10.903661.499914055 1.66670486663317 2.33340973326635 1.503942 1.074234 10.903661.499914056 1.66670486618868 2.33340973237736 1.503942 1.074234 10.903661.499914057 1.66670486574418 2.33340973148837 1.503942 1.074234 10.903661.499914058 1.66670486529969 2.33340973059938 1.503942 1.074234 10.903661.499914059 1.66670486485519 2.33340972971039 1.503942 1.074234 10.90366

β Δ Г(n)1.499914051 0.0000 0.9027516202213

Média (μ) Desvio Padrão (σ) Variância (σ²)

P0

P1

P2

P3

P4

P5

N1(1+(1/β)) N2(1+(2/β)) √(2π)/N1 √(2π)/N2

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Г(n) λ0.90275162022 3.02271240997279E-05

10229.96

Г(n)PARCELA Ps2 Parcela 1 = Parcela 2 = e8.19935028441 71.3222397965415 341.1371638 0.00077186 0.000396272 0.902752 1.1906968.19935028713 71.3222397245207 341.1371631 0.00077186 0.000396272 0.902752 1.1906968.19935028985 71.3222396525 341.1371623 0.00077186 0.000396272 0.902752 1.1906968.19935029258 71.3222395804792 341.1371616 0.00077186 0.000396272 0.902752 1.190696

8.1993502953 71.3222395084584 341.1371609 0.00077186 0.000396272 0.902752 1.1906968.19935029802 71.3222394364377 341.1371601 0.00077186 0.000396272 0.902752 1.1906968.19935030075 71.322239364417 341.1371594 0.00077186 0.000396272 0.902752 1.1906968.19935030347 71.3222392923962 341.1371587 0.00077186 0.000396272 0.902752 1.1906968.19935030619 71.3222392203755 341.1371579 0.00077186 0.000396272 0.902752 1.1906968.19935030891 71.3222391483547 341.1371572 0.00077186 0.000396272 0.902752 1.1906968.19935031164 71.3222390763339 341.1371565 0.00077186 0.000396272 0.902752 1.1906968.19935031436 71.3222390043133 341.1371557 0.00077186 0.000396272 0.902752 1.1906968.19935031708 71.3222389322925 341.137155 0.00077186 0.000396272 0.902752 1.190696

8.1993503198 71.3222388602717 341.1371543 0.00077186 0.000396272 0.902752 1.1906968.19935032253 71.322238788251 341.1371535 0.00077186 0.000396272 0.902752 1.1906968.19935032525 71.3222387162303 341.1371528 0.00077186 0.000396272 0.902752 1.1906968.19935032797 71.3222386442095 341.1371521 0.00077186 0.000396272 0.902752 1.190696

8.1993503307 71.3222385721888 341.1371513 0.00077186 0.000396272 0.902752 1.1906968.19935033342 71.322238500168 341.1371506 0.00077186 0.000396272 0.902752 1.1906968.19935033614 71.3222384281472 341.1371499 0.00077186 0.000396272 0.902752 1.190696

Parcela 1 = (N+5,5)N+0,5 Parcela 2 = (N+5,5)N+0,5 Г(N1) Г(N2)

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399360.156095103 0.0054 1.499914 0.902752399360.155604335 0.0049 1.499914 0.902752399360.155113568 0.0044 1.499914 0.902752

399360.1546228 0.0039 1.499914 0.902752399360.154132029 0.0034 1.499914 0.902752

399360.15364126 0.0029 1.499914 0.902752399360.153150494 0.0024 1.499914 0.902752399360.152659725 0.0019 1.499914 0.902752399360.152168955 0.0014 1.499914 0.902752399360.151678187 0.0009 1.499914 0.902752399360.151187416 0.0004 1.499914 0.902752399360.150696648 0.0000 1.499914 0.902752

399360.15020588 0.0005 1.499914 0.902752399360.149715111 0.0010 1.499914 0.902752399360.149224342 0.0015 1.499914 0.902752399360.148733575 0.0020 1.499914 0.902752399360.148242805 0.0025 1.499914 0.902752399360.147752036 0.0030 1.499914 0.902752399360.147261269 0.0035 1.499914 0.902752399360.146770499 0.0040 1.499914 0.902752

Variância (σ²) Variação (Δ)

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z0.0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

1 2 3 4 5 6 7 8

0.0 1 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279

0.1 2 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675

0.2 3 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064

0.3 4 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443

0.4 5 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808

0.5 6 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157

0.6 7 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486

0.7 8 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794

0.8 9 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078

0.9 10 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340

1.0 11 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577

1.1 12 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790

1.2 13 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980

1.3 14 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147

1.4 15 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292

1.5 16 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418

1.6 17 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525

1.7 18 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616

1.8 19 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693

1.9 20 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756

2.0 21 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808

2.1 22 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850

2.2 23 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884

2.3 24 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911

2.4 25 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932

2.5 26 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949

2.6 27 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962

2.7 28 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972

2.8 29 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979

2.9 30 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985

3.0 31 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989

3.1 32 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992

3.2 33 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995

3.3 34 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996

3.4 35 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997

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3.5 36 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998

3.6 37 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

3.7 38 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

3.8 39 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

3.9 40 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

z1 2 3 4 5 6 7 8

0.0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Page 20: I VA -Número 2

0.08 0.09z9 10

0.5319 0.5359 1 0.0

0.5714 0.5753 2 0.1

0.6103 0.6141 3 0.2

0.6480 0.6517 4 0.3

0.6844 0.6879 5 0.4

0.7190 0.7224 6 0.5

0.7517 0.7549 7 0.6

0.7823 0.7852 8 0.7

0.8106 0.8133 9 0.8

0.8365 0.8389 10 0.9

0.8599 0.8621 11 1.0

0.8810 0.8830 12 1.1

0.8997 0.9015 13 1.2

0.9162 0.9177 14 1.3

0.9306 0.9319 15 1.4

0.9429 0.9441 16 1.5

0.9535 0.9545 17 1.6

0.9625 0.9633 18 1.7

0.9699 0.9706 19 1.8

0.9761 0.9767 20 1.9

0.9812 0.9817 21 2.0

0.9854 0.9857 22 2.1

0.9887 0.9890 23 2.2

0.9913 0.9916 24 2.3

0.9934 0.9936 25 2.4

0.9951 0.9952 26 2.5

0.9963 0.9964 27 2.6

0.9973 0.9974 28 2.7

0.9980 0.9981 29 2.8

0.9986 0.9986 30 2.9

0.9990 0.9990 31 3.0

0.9993 0.9993 32 3.1

0.9995 0.9995 33 3.2

0.9996 0.9997 34 3.3

0.9997 0.9998 35 3.4

Page 21: I VA -Número 2

0.9998 0.9998 36 3.5

0.9999 0.9999 37 3.6

0.9999 0.9999 38 3.7

0.9999 0.9999 39 3.8

1.0000 1.0000 40 3.9

9 10z0.08 0.09

Page 22: I VA -Número 2

z0.0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

1 2 3 4 5 6 7 8

0.0 1 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721

-0.1 2 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325

-0.2 3 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936

-0.3 4 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557

-0.4 5 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192

-0.5 6 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843

-0.6 7 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514

-0.7 8 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206

-0.8 9 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922

-0.9 10 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660

-1.0 11 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423

-1.1 12 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210

-1.2 13 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020

-1.3 14 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853

-1.4 15 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708

-1.5 16 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582

-1.6 17 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475

-1.7 18 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384

-1.8 19 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307

-1.9 20 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244

-2.0 21 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192

-2.1 22 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150

-2.2 23 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116

-2.3 24 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089

-2.4 25 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068

-2.5 26 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051

-2.6 27 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038

-2.7 28 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028

-2.8 29 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021

-2.9 30 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015

-3.0 31 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011

-3.1 32 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008

-3.2 33 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005

-3.3 34 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004

-3.4 35 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003

-3.5 36 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002

P(Z<z)

Page 23: I VA -Número 2

-3.6 37 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001

-3.7 38 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001

-3.8 39 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001

-3.9 40 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

1 2 3 4 5 6 7 8

Page 24: I VA -Número 2

0.08 0.09

z9 10

0.4681 0.4641 1 0.0

0.4286 0.4247 2 -0.1

0.3897 0.3859 3 -0.2

0.3520 0.3483 4 -0.3

0.3156 0.3121 5 -0.4

0.2810 0.2776 6 -0.5

0.2483 0.2451 7 -0.6

0.2177 0.2148 8 -0.7

0.1894 0.1867 9 -0.8

0.1635 0.1611 10 -0.9

0.1401 0.1379 11 -1.0

0.1190 0.1170 12 -1.1

0.1003 0.0985 13 -1.2

0.0838 0.0823 14 -1.3

0.0694 0.0681 15 -1.4

0.0571 0.0559 16 -1.5

0.0465 0.0455 17 -1.6

0.0375 0.0367 18 -1.7

0.0301 0.0294 19 -1.8

0.0239 0.0233 20 -1.9

0.0188 0.0183 21 -2.0

0.0146 0.0143 22 -2.1

0.0113 0.0110 23 -2.2

0.0087 0.0084 24 -2.3

0.0066 0.0064 25 -2.4

0.0049 0.0048 26 -2.5

0.0037 0.0036 27 -2.6

0.0027 0.0026 28 -2.7

0.0020 0.0019 29 -2.8

0.0014 0.0014 30 -2.9

0.0010 0.0010 31 -3.0

0.0007 0.0007 32 -3.1

0.0005 0.0005 33 -3.2

0.0004 0.0003 34 -3.3

0.0003 0.0002 35 -3.4

0.0002 0.0002 36 -3.5

Page 25: I VA -Número 2

0.0001 0.0001 37 -3.6

0.0001 0.0001 38 -3.7

0.0001 0.0001 39 -3.8

0.0000 0.0000 40 -3.9

9 10