8/17/2019 2.1.1 Tabla normal.pdf

1/4

 

293

Áreas bajo la curva normal estándara seis dígitos decimales  

(los dos dígitos de la primera fila son los

centésimos de cada valor de z)

∫ ∞−

−=Φ

 z x

dx z e

2

2

1

2

1)(

π 

 

 z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09

−−−−3.6 .000159 .000153 .000147 .000142 .000136 .000131 .000126 .000121 .000117 .000112−−−−3.5 .000233 .000224 .000216 .000208 .000200 .000193 .000185 .000179 .000172 .000165−−−−3.4 .000337 .000325 .000313 .000302 .000291 .000280 .000270 .000260 .000251 .000242−−−−3.3 .000483 .000467 .000450 .000434 .000419 .000404 .000390 .000376 .000362 .000350−−−−3.2 .000687 .000664 .000641 .000619 .000598 .000577 .000557 .000538 .000519 .000501−−−−3.1 .000968 .000936 .000904 .000874 .000845 .000816 .000789 .000762 .000736 .000711−−−−3.0 .001350 .001306 .001264 .001223 .001183 .001144 .001107 .001070 .001035 .001001−−−−2.9 .001866 .001807 .001750 .001695 .001641 .001589 .001538 .001489 .001441 .001395−−−−2.8 .002555 .002477 .002401 .002327 .002256 .002186 .002118 .002052 .001988 .001926−−−−2.7 .003467 .003364 .003264 .003167 .003072 .002980 .002890 .002803 .002718 .002635−−−−2.6 .004661 .004527 .004397 .004269 .004145 .004025 .003907 .003793 .003681 .003573−−−−2.5 .006210 .006037 .005868 .005703 .005543 .005386 .005234 .005085 .004940 .004799

−−−−2.4 .008198 .007976 .007760 .007549 .007344 .007143 .006947 .006756 .006569 .006387−−−−2.3 .010724 .010444 .010170 .009903 .009642 .009387 .009137 .008894 .008656 .008424−−−−2.2 .013903 .013553 .013209 .012874 .012545 .012224 .011911 .011604 .011304 .011011−−−−2.1 .017864 .017429 .017003 .016586 .016177 .015778 .015386 .015003 .014629 .014262−−−−2.0 .022750 .022216 .021692 .021178 .020675 .020182 .019699 .019226 .018763 .018309−−−−1.9 .028716 .028067 .027429 .026803 .026190 .025588 .024998 .024419 .023852 .023295−−−−1.8 .035930 .035148 .034379 .033625 .032884 .032157 .031443 .030742 .030054 .029379−−−−1.7 .044565 .043633 .042716 .041815 .040929 .040059 .039204 .038364 .037538 .036727−−−−1.6 .054799 .053699 .052616 .051551 .050503 .049471 .048457 .047460 .046479 .045514−−−−1.5 .066807 .065522 .064256 .063008 .061780 .060571 .059380 .058208 .057053 .055917−−−−1.4 .080757 .079270 .077804 .076359 .074934 .073529 .072145 .070781 .069437 .068112−−−−1.3 .096801 .095098 .093418 .091759 .090123 .088508 .086915 .085344 .083793 .082264

−−−−1.2 .115070 .113140 .111233 .109349 .107488 .105650 .103835 .102042 .100273 .098525−−−−1.1 .135666 .133500 .131357 .129238 .127143 .125072 .123024 .121001 .119000 .117023−−−−1.0 .158655 .156248 .153864 .151505 .149170 .146859 .144572 .142310 .140071 .137857−−−−0.9 .184060 .181411 .178786 .176186 .173609 .171056 .168528 .166023 .163543 .161087−−−−0.8 .211855 .208970 .206108 .203269 .200454 .197662 .194894 .192150 .189430 .186733−−−−0.7 .241964 .238852 .235762 .232695 .229650 .226627 .223627 .220650 .217695 .214764−−−−0.6 .274253 .270931 .267629 .264347 .261086 .257846 .254627 .251429 .248252 .245097−−−−0.5 .308538 .305026 .301532 .298056 .294598 .291160 .287740 .284339 .280957 .277595

 Para valores de  z fuera del intervalo que abarca desde −−−−3.69 a 3.69, consúltese la tabla adjunta 

8/17/2019 2.1.1 Tabla normal.pdf

2/4

 

294

Áreas bajo la curva normal estándar (continuación).

 z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09

−−−−0.4 .344578 .340903 .337243 .333598 .329969 .326355 .322758 .319178 .315614 .312067−−−−0.3 .382089 .378281 .374484 .370700 .366928 .363169 .359424 .355691 .351973 .348268−−−−0.2 .420740 .416834 .412936 .409046 .405165 .401294 .397432 .393580 .389739 .385908−−−−0.1 .460172 .456205 .452242 .448283 .444330 .440382 .436441 .432505 .428576 .424655−0.0 .500000 .496011 .492022 .488033 .484047 .480061 .476078 .472097 .468119 .4641440.0 .500000 .503989 .507978 .511967 .515953 .519939 .523922 .527903 .531881 .5358560.1 .539828 .543795 .547758 .551717 .555670 .559618 .563559 .567495 .571424 .5753450.2 .579260 .583166 .587064 .590954 .594835 .598706 .602568 .606420 .610261 .614092

0.3 .617911 .621719 .625516 .629300 .633072 .636831 .640576 .644309 .648027 .6517320.4 .655422 .659097 .662757 .666402 .670031 .673645 .677242 .680822 .684386 .6879330.5 .691462 .694974 .698468 .701944 .705402 .708840 .712260 .715661 .719043 .7224050.6 .725747 .729069 .732371 .735653 .738914 .742154 .745373 .748571 .751748 .7549030.7 .758036 .761148 .764238 .767305 .770350 .773373 .776373 .779350 .782305 .7852360.8 .788145 .791030 .793892 .796731 .799546 .802338 .805106 .807850 .810570 .8132670.9 .815940 .818589 .821214 .823814 .826391 .828944 .831472 .833977 .836457 .8389131.0 .841345 .843752 .846136 .848495 .850830 .853141 .855428 .857690 .859929 .8621431.1 .864334 .866500 .868643 .870762 .872857 .874928 .876976 .878999 .881000 .8829771.2 .884930 .886860 .888767 .890651 .892512 .894350 .896165 .897958 .899727 .9014751.3 .903199 .904902 .906582 .908241 .909877 .911492 .913085 .914656 .916207 .9177361.4 .919243 .920730 .922196 .923641 .925066 .926471 .927855 .929219 .930563 .9318881.5 .933193 .934478 .935744 .936992 .938220 .939429 .940620 .941792 .942947 .9440831.6 .945201 .946301 .947384 .948449 .949497 .950529 .951543 .952540 .953521 .9544861.7 .955435 .956367 .957284 .958185 .959071 .959941 .960796 .961636 .962462 .9632731.8 .964070 .964852 .965621 .966375 .967116 .967843 .968557 .969258 .969946 .9706211.9 .971284 .971933 .972571 .973197 .973810 .974412 .975002 .975581 .976148 .9767052.0 .977250 .977784 .978308 .978822 .979325 .979818 .980301 .980774 .981237 .9816912.1 .982136 .982571 .982997 .983414 .983823 .984222 .984614 .984997 .985371 .9857382.2 .986097 .986447 .986791 .987126 .987455 .987776 .988089 .988396 .988696 .9889892.3 .989276 .989556 .989830 .990097 .990358 .990613 .990863 .991106 .991344 .9915762.4 .991802 .992024 .992240 .992451 .992656 .992857 .993053 .993244 .993431 .9936132.5 .993790 .993963 .994132 .994297 .994457 .994614 .994766 .994915 .995060 .9952012.6 .995339 .995473 .995603 .995731 .995855 .995975 .996093 .996207 .996319 .9964272.7 .996533 .996636 .996736 .996833 .996928 .997020 .997110 .997197 .997282 .997365

2.8 .997445 .997523 .997599 .997673 .997744 .997814 .997882 .997948 .998012 .9980742.9 .998134 .998193 .998250 .998305 .998359 .998411 .998462 .998511 .998559 .9986053.0 .998650 .998694 .998736 .998777 .998817 .998856 .998893 .998930 .998965 .9989993.1 .999032 .999064 .999096 .999126 .999155 .999184 .999211 .999238 .999264 .9992893.2 .999313 .999336 .999359 .999381 .999402 .999423 .999443 .999462 .999481 .9994993.3 .999517 .999533 .999550 .999566 .999581 .999596 .999610 .999624 .999638 .9996503.4 .999663 .999675 .999687 .999698 .999709 .999720 .999730 .999740 .999749 .9997583.5 .999767 .999776 .999784 .999792 .999800 .999807 .999815 .999821 .999828 .9998353.6 .999841 .999847 .999853 .999858 .999864 .999869 .999874 .999879 .999883 .999888

8/17/2019 2.1.1 Tabla normal.pdf

3/4

8/17/2019 2.1.1 Tabla normal.pdf

4/4

 

296

Tabla adjunta de áreas bajo la curva normal para valores de  z muy alejados del cero.

(continuación).

 z Φ( z)  z  Φ( z)  z  Φ( z)  z  Φ( z)−−−−4.48 3.735508×10−−−−6  −−−−4.28 9.351183×10−−−−6  −−−−4.08 2.252972×10−−−−5  −−−−3.88 5.224838×10−−−−5 −−−−4.47  3.914454×10−−−−6  −−−−4.27  9.780374×10−−−−6  −−−−4.07  2.351877×10−−−−5  −−−−3.87  5.443833×10−−−−5 −−−−4.46  4.101579×10−−−−6  −−−−4.26  1.022828×10−−−−5  −−−−4.06  2.454891×10−−−−5  −−−−3.86  5.671467×10−−−−5 −−−−4.45  4.297236×10−−−−6  −−−−4.25  1.069569×10−−−−5  −−−−4.05  2.562172×10−−−−5  −−−−3.85  5.908059×10−−−−5 −−−−4.44  4.501795×10−−−−6  −−−−4.24  1.118337×10−−−−5  −−−−4.04  2.673887×10−−−−5  −−−−3.84  6.153936×10−−−−5 

−−−−4.43  4.715639×10−−−−6

  −−−−4.23  1.169218×10−−−−5

  −−−−4.03  2.790206×10−−−−5

  −−−−3.83  6.409437×10−−−−5

 −−−−4.42  4.939167×10−−−−6  −−−−4.22  1.222297×10−−−−5  −−−−4.02  2.911308×10−−−−5  −−−−3.82  6.674912×10−−−−5 −−−−4.41  5.172795×10−−−−6  −−−−4.21  1.277663×10−−−−5  −−−−4.01  3.037377×10−−−−5  −−−−3.81  6.950723×10−−−−5 −−−−4.40  5.416953×10−−−−6  −−−−4.20  1.335410×10−−−−5  −−−−4.00  3.168603×10−−−−5  −−−−3.80  7.237243×10−−−−5 −−−−4.39  5.672092×10−−−−6  −−−−4.19  1.395633×10−−−−5  −−−−3.99  3.305184×10−−−−5  −−−−3.79  7.534860×10−−−−5 −−−−4.38  5.938679×10−−−−6  −−−−4.18  1.458432×10−−−−5  −−−−3.98  3.447324×10−−−−5  −−−−3.78  7.843971×10−−−−5 −−−−4.37  6.217199×10−−−−6  −−−−4.17  1.523912×10−−−−5  −−−−3.97  3.595234×10−−−−5  −−−−3.77  8.164989×10−−−−5 −−−−4.36  6.508157×10−−−−6  −−−−4.16  1.592179×10−−−−5  −−−−3.96  3.749133×10−−−−5  −−−−3.76  8.498338×10−−−−5 −−−−4.35  6.812079×10−−−−6  −−−−4.15  1.663346×10−−−−5  −−−−3.95  3.909248×10−−−−5  −−−−3.75  8.844459×10−−−−5 −−−−4.34  7.129511×10−−−−6  −−−−4.14  1.737527×10−−−−5  −−−−3.94  4.075813×10−−−−5  −−−−3.74  9.203804×10−−−−5 −−−−4.33  7.461020×10−−−−6  −−−−4.13  1.814844×10−−−−5  −−−−3.93  4.249070×10−−−−5  −−−−3.73  9.576841×10−−−−5 

−−−−4.32  7.807196×10−−−−6  −−−−4.12  1.895420×10−−−−5  −−−−3.92  4.429272×10−−−−5  −−−−3.72  9.964054×10−−−−5 −−−−4.31  8.168650×10−−−−6  −−−−4.11  1.979385×10−−−−5  −−−−3.91  4.616676×10−−−−5  −−−−3.71  1.036594×10−−−−4 −−−−4.30  8.546021×10−−−−6  −−−−4.10  2.066872×10−−−−5  −−−−3.90  4.811552×10−−−−5  −−−−3.70  1.078301×10−−−−4 −−−−4.29  8.939969×10−−−−6  −−−−4.09  2.158019×10−−−−5  −−−−3.89  5.014177×10−−−−5  −−−−3.69  1.121581×10−−−−4