Transcription of DISTRIBUCION NORMAL - Estadística
1 DISTRIBUCION NORMAL . Jorge M. Galbiati Funci . on de probabilidad: 1 (x )2 . p(x) = exp para x ( , + ). (2 ) 2 2. Espacio param . etrico: media ( , + ) varianza 2 . (0, + ). Valor esperado: . Varianza: 2. 2 2. Funci . on generadora de momentos: e( t+ t /2). f(y). F(x). 0 x y DISTRIBUCION NORMAL ESTANDAR. Es un caso especial de la NORMAL , en que = 0 y 2 = 1. Funci . on de densidad: 1 x2 . f (x) = exp para x ( , + ). (2 ) 2. Valor esperado: 0. Varianza: 1. 2. Funci . on generadora de momentos: et /2. RELACION CON LA NORMAL ESTANDAR. Los valores de la funci on de distribuci on de la NORMAL con par ametros y 2 se obtienen de la tabla de distribuci on NORMAL standard (en que = 0 y 2 =1) como se muestra a continuaci on.
2 Por esa raz on s olo se entrega la tabla de la NORMAL standard. Si se requiere la probabilidad acumulada hasta la cuantila x, se efect . ua la transformaci on z = x y se busca la probabilidad asociada a la cuantila z en la tabla de distribuci on NORMAL standard. Al rev es, si se quiere saber a qu e cuantila corresponde una probabilidad acumulada dada, F (z), se busca la cuantila z asociada a F (z) en la tabla de distribuci on NORMAL standard. Entonces la correspondiente cuantila de la NORMAL con par ametros y 2 es x = z + . TABLA DE DISTRIBUCION NORMAL ESTANDAR.
3 La tabla entrega valores de la funci on de distribuci on (probabilidad acumulada). z de la NORMAL standard, es decir, valores de F (z) =. f (y)dy . La cuantila z toma valores entre -4 y +4 variando en El entero y el primer decimal aparecen en el margen izquierdo. Los dos u ltimos decimales en el margen superior. Las probabilidades acu- muladas aparecen en el cuerpo de la tabla. TABLA DE DISTRIBUCION NORMAL . Cuantiles negativos z -95 -90 -85 -80 -75 -70 -65 -60 -55 -50..0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000..0000 .0000 .0000 .0000 .0000.
4 0000 .0000 .0000 .0000 .0000..0000 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001..0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001..0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001..0002 .0002 .0002 .0002 .0002 .0002 .0002 .0002 .0002 .0002..0002 .0002 .0002 .0003 .0003 .0003 .0003 .0003 .0003 .0003..0003 .0003 .0004 .0004 .0004 .0004 .0004 .0004 .0004 .0004..0005 .0005 .0005 .0005 .0005 .0005 .0005 .0006 .0006 .0006..0007 .0007 .0007 .0007 .0007 .0008 .0008 .0008 .0008 .0008..0010 .0010 .0010 .0010 .0011 .0011 .0011 .0011 .0011.
5 0011..0014 .0014 .0014 .0014 .0015 .0015 .0015 .0015 .0016 .0016..0019 .0019 .0020 .0020 .0020 .0021 .0021 .0021 .0022 .0022..0026 .0026 .0027 .0027 .0028 .0028 .0028 .0029 .0029 .0030..0035 .0036 .0036 .0037 .0037 .0038 .0038 .0039 .0040 .0040..0047 .0048 .0049 .0049 .0050 .0051 .0052 .0052 .0053 .0054..0063 .0064 .0065 .0066 .0067 .0068 .0069 .0069 .0070 .0071..0083 .0084 .0085 .0087 .0088 .0089 .0090 .0091 .0093 .0094..0109 .0110 .0112 .0113 .0115 .0116 .0118 .0119 .0121 .0122..0141 .0143 .0144 .0146 .0148 .0150 .0152 .0154 .0156 .0158..0181 .0183 .0185.
6 0188 .0190 .0192 .0195 .0197 .0199 .0202..0230 .0233 .0236 .0239 .0241 .0244 .0247 .0250 .0253 .0256..0290 .0294 .0297 .0301 .0304 .0307 .0311 .0314 .0318 .0322..0363 .0367 .0371 .0375 .0379 .0384 .0388 .0392 .0396 .0401..0450 .0455 .0460 .0465 .0470 .0475 .0480 .0485 .0490 .0495..0554 .0559 .0565 .0571 .0576 .0582 .0588 .0594 .0600 .0606..0675 .0681 .0688 .0694 .0701 .0708 .0715 .0721 .0728 .0735..0815 .0823 .0830 .0838 .0846 .0853 .0861 .0869 .0877 .0885..0977 .0985 .0994 .1003 .1012 .1020 .1029 .1038 .1047 .1056..1160 .1170 .1180 .1190 .1200 .1210 .1220.
7 1230 .1240 .1251..1368 .1379 .1390 .1401 .1412 .1423 .1434 .1446 .1457 .1469..1599 .1611 .1623 .1635 .1648 .1660 .1673 .1685 .1698 .1711..1854 .1867 .1881 .1894 .1908 .1922 .1935 .1949 .1963 .1977..2133 .2148 .2162 .2177 .2192 .2206 .2221 .2236 .2251 .2266..2435 .2451 .2467 .2483 .2498 .2514 .2530 .2546 .2562 .2578..2759 .2776 .2793 .2810 .2826 .2843 .2860 .2877 .2894 .2912..3103 .3121 .3138 .3156 .3174 .3192 .3210 .3228 .3246 .3264..3464 .3483 .3501 .3520 .3538 .3557 .3576 .3594 .3613 .3632..3840 .3859 .3878 .3897 .3917 .3936 .3955 .3974 .3994 .4013..4227.
8 4247 .4266 .4286 .4305 .4325 .4345 .4364 .4384 .4404..4622 .4641 .4661 .4681 .4701 .4721 .4741 .4761 .4781 .4801. DISTRIBUCION NORMAL (2). Cuantiles negativos z -45 -40 -35 -30 -25 -20 -15 -10 -05 -00..0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000..0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000..0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001..0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001..0001 .0001 .0001 .0001 .0001 .0001 .0002 .0002 .0002 .0002..0002 .0002 .0002 .0002 .0002 .0002 .0002 .0002 .0002 .0002.
9 0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003..0004 .0004 .0004 .0004 .0004 .0005 .0005 .0005 .0005 .0005..0006 .0006 .0006 .0006 .0006 .0006 .0007 .0007 .0007 .0007..0008 .0008 .0009 .0009 .0009 .0009 .0009 .0009 .0010 .0010..0012 .0012 .0012 .0012 .0012 .0013 .0013 .0013 .0013 .0013..0016 .0016 .0017 .0017 .0017 .0018 .0018 .0018 .0018 .0019..0022 .0023 .0023 .0023 .0024 .0024 .0024 .0025 .0025 .0026..0030 .0031 .0031 .0032 .0032 .0033 .0033 .0034 .0034 .0035..0041 .0041 .0042 .0043 .0043 .0044 .0045 .0045 .0046 .0047..0055 .0055 .0056 .0057.
10 0058 .0059 .0060 .0060 .0061 .0062..0072 .0073 .0074 .0075 .0077 .0078 .0079 .0080 .0081 .0082..0095 .0096 .0098 .0099 .0100 .0102 .0103 .0104 .0106 .0107..0124 .0125 .0127 .0129 .0130 .0132 .0134 .0136 .0137 .0139..0160 .0162 .0164 .0166 .0168 .0170 .0172 .0174 .0176 .0179..0204 .0207 .0209 .0212 .0214 .0217 .0220 .0222 .0225 .0228..0259 .0262 .0265 .0268 .0271 .0274 .0277 .0281 .0284 .0287..0325 .0329 .0333 .0336 .0340 .0344 .0348 .0351 .0355 .0359..0405 .0409 .0414 .0418 .0423 .0427 .0432 .0436 .0441 .0446..0500 .0505 .0510 .0516 .0521 .0526 .0532 .0537.
