Niffs

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Distribución normal estándar

[pic]
Esta curva "de campana" es la distribución normal estándar.
Puedes usar la tabla de abajo para saber el área bajo la curva desde la línea central hasta cualquier línea vertical "a valor Z" hasta 3, en incrementos de 0.1
Esto te dice qué parte de la población está dentro de "Z" desviaciones estándar de la media. En lugar de una tabla LARGA, hemos puestolos incrementos de 0.1 hacia abajo, y los de 0.01 de lado. Por ejemplo, para saber el área debajo de la curva entre 0 y 0.45, ve a la fila de 0.4, y sigue de lado hasta 0.45, allí pone 0.1736
Como la curva es simétrica, la tabla vale para ir en las dos direcciones, así que 0.45 negativo también tiene un área de 0.1736
Z |0.00 |0.01 |0.02 |0.03 |0.04 |0.05 |0.06 |0.07 |0.08 |0.09 | |0.0 |0.0000|0.0040 |0.0080 |0.0120 |0.0160 |0.0199 |0.0239 |0.0279 |0.0319 |0.0359 | |0.1 |0.0398 |0.0438 |0.0478 |0.0517 |0.0557 |0.0596 |0.0636 |0.0675 |0.0714 |0.0753 | |0.2 |0.0793 |0.0832 |0.0871 |0.0910 |0.0948 |0.0987 |0.1026 |0.1064 |0.1103 |0.1141 | |0.3 |0.1179 |0.1217 |0.1255 |0.1293 |0.1331 |0.1368 |0.1406 |0.1443 |0.1480 |0.1517 | |0.4 |0.1554 |0.1591 |0.1628 |0.1664 |0.1700 |0.1736 |0.1772 |0.1808|0.1844 |0.1879 | |0.5 |0.1915 |0.1950 |0.1985 |0.2019 |0.2054 |0.2088 |0.2123 |0.2157 |0.2190 |0.2224 | |0.6 |0.2257 |0.2291 |0.2324 |0.2357 |0.2389 |0.2422 |0.2454 |0.2486 |0.2517 |0.2549 | |0.7 |0.2580 |0.2611 |0.2642 |0.2673 |0.2704 |0.2734 |0.2764 |0.2794 |0.2823 |0.2852 | |0.8 |0.2881 |0.2910 |0.2939 |0.2967 |0.2995 |0.3023 |0.3051 |0.3078 |0.3106 |0.3133 | |0.9 |0.3159 |0.3186 |0.3212|0.3238 |0.3264 |0.3289 |0.3315 |0.3340 |0.3365 |0.3389 | |1.0 |0.3413 |0.3438 |0.3461 |0.3485 |0.3508 |0.3531 |0.3554 |0.3577 |0.3599 |0.3621 | |1.1 |0.3643 |0.3665 |0.3686 |0.3708 |0.3729 |0.3749 |0.3770 |0.3790 |0.3810 |0.3830 | |1.2 |0.3849 |0.3869 |0.3888 |0.3907 |0.3925 |0.3944 |0.3962 |0.3980 |0.3997 |0.4015 | |1.3 |0.4032 |0.4049 |0.4066 |0.4082 |0.4099 |0.4115 |0.4131 |0.4147 |0.4162 |0.4177| |1.4 |0.4192 |0.4207 |0.4222 |0.4236 |0.4251 |0.4265 |0.4279 |0.4292 |0.4306 |0.4319 | |1.5 |0.4332 |0.4345 |0.4357 |0.4370 |0.4382 |0.4394 |0.4406 |0.4418 |0.4429 |0.4441 | |1.6 |0.4452 |0.4463 |0.4474 |0.4484 |0.4495 |0.4505 |0.4515 |0.4525 |0.4535 |0.4545 | |1.7 |0.4554 |0.4564 |0.4573 |0.4582 |0.4591 |0.4599 |0.4608 |0.4616 |0.4625 |0.4633 | |1.8 |0.4641 |0.4649 |0.4656 |0.4664 |0.4671|0.4678 |0.4686 |0.4693 |0.4699 |0.4706 | |1.9 |0.4713 |0.4719 |0.4726 |0.4732 |0.4738 |0.4744 |0.4750 |0.4756 |0.4761 |0.4767 | |2.0 |0.4772 |0.4778 |0.4783 |0.4788 |0.4793 |0.4798 |0.4803 |0.4808 |0.4812 |0.4817 | |2.1 |0.4821 |0.4826 |0.4830 |0.4834 |0.4838 |0.4842 |0.4846 |0.4850 |0.4854 |0.4857 | |2.2 |0.4861 |0.4864 |0.4868 |0.4871 |0.4875 |0.4878 |0.4881 |0.4884 |0.4887 |0.4890 | |2.3 |0.4893|0.4896 |0.4898 |0.4901 |0.4904 |0.4906 |0.4909 |0.4911 |0.4913 |0.4916 | |2.4 |0.4918 |0.4920 |0.4922 |0.4925 |0.4927 |0.4929 |0.4931 |0.4932 |0.4934 |0.4936 | |2.5 |0.4938 |0.4940 |0.4941 |0.4943 |0.4945 |0.4946 |0.4948 |0.4949 |0.4951 |0.4952 | |2.6 |0.4953 |0.4955 |0.4956 |0.4957 |0.4959 |0.4960 |0.4961 |0.4962 |0.4963 |0.4964 | |2.7 |0.4965 |0.4966 |0.4967 |0.4968 |0.4969 |0.4970 |0.4971|0.4972 |0.4973 |0.4974 | |2.8 |0.4974 |0.4975 |0.4976 |0.4977 |0.4977 |0.4978 |0.4979 |0.4979 |0.4980 |0.4981 | |2.9 |0.4981 |0.4982 |0.4982 |0.4983 |0.4984 |0.4984 |0.4985 |0.4985 |0.4986 |0.4986 | |3.0 |0.4987 |0.4987 |0.4987 |0.4988 |0.4988 |0.4989 |0.4989 |0.4989 |0.4990 |0.4990 | |
La distribución normal tipificada tiene por función de densidad:
[pic]
[pic]
La función de distribuciónpara [pic], seria:
[pic]
donde:
[pic]
La tabla distribución normal tipificada, presenta las soluciones a esta integral para distintos valores de x, hay varios modelos de tablas de este tipo, así como algoritmos para su cálculo por ordenador, podemos ver un ejemplo de este tipo de tablas.
La distribución normal tiene por función de densidad:
[pic]
que depende de dos...
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