{"id":2306,"date":"2021-04-01T20:20:46","date_gmt":"2021-04-01T20:20:46","guid":{"rendered":"https:\/\/ricovictor.com\/?p=2306"},"modified":"2026-01-29T21:52:14","modified_gmt":"2026-01-29T21:52:14","slug":"distribucion-normal-en-r","status":"publish","type":"post","link":"https:\/\/ricovictor.com\/index.php\/2021\/04\/01\/distribucion-normal-en-r\/","title":{"rendered":"Distribuci\u00f3n Normal en R"},"content":{"rendered":"\t\t
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La Distribuci\u00f3n <\/strong><\/span>Normal<\/strong>\u200b<\/span> es la m\u00e1s importante de las distribuciones<\/a> continuas<\/strong>, debido a la gran cantidad de fen\u00f3menos reales en la que se usa.<\/span> Esta distribuci\u00f3n tambi\u00e9n se conoce como gaussiana o de <\/span>Gauss\u200b<\/span>, en honor a su descubridor. <\/span><\/p>

SI nos fijamos en su forma cabe destacar que es sim\u00e9trica y tiene forma de campana. Adem\u00e1s, est\u00e1 delimitada por solamente 2 par\u00e1metros, uno es la media aritm\u00e9tica y el otro la desviaci\u00f3n t\u00edpica.<\/span><\/p>

De manera que definiremos la variable aleatoria X y su distribuci\u00f3n como sigue: <\/span><\/p>

X \u2192 N(\u03bc, \u03c3) <\/span><\/strong><\/p>

En este tutorial podr\u00e1s ver ejemplos del uso de este tipo de distribuci\u00f3n apoy\u00e1ndonos en el software R. Debajo tienen el c\u00f3digo con los ejemplos<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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C\u00d3DIGO EN R DEL V\u00cdDEO<\/strong><\/h4>

\u00a0<\/p>

\u00a0<\/p>

## DISTRIBUCI\u00d3N NORMAL EN R<\/p>

# Ejemplo n\u00fameros aleatorios<\/p>

R_normal <- rnorm(500, mean = 0, sd = 1)
R_normal<\/p>

hist(R_normal)<\/p>

R_normal <- rnorm(500, mean = 2, sd = 2.5)<\/p>

hist(R_normal)<\/p>

####<\/p>

#pnorm(q, mean = ?, sd = ?)<\/p>

#qnorm(p, mean = ?, sd = ?)<\/p>

## Ejemplo 1<\/p>

## El nivel de colesterol en una persona adulta sana sigue
# una Distribuci\u00f3n normal N(192,12)
# Calcula la probabilidad de que una persona tenga un nivel de Colesterol<\/p>

# A) Superior a 200<\/p>

# P ( X>200) = 1 – P(X<=200)<\/p>

1 – pnorm(200, mean = 192, sd = 12)<\/p>

pnorm(200, mean = 192, sd = 12) #P X>200<\/p>

1-0.7475075<\/p>

# B) entre 180 y 220<\/p>

# P( 180 <= X <= 220)<\/p>

# P[X \u2264 220] \u2013 P[ X \u2264 180]<\/p>

pnorm(c(220, 180), mean = 192, sd = 12)<\/p>

0.9901847- 0.1586553<\/p>

0.8315294<\/p>

# c la cantidad m\u00ednima de colesterol que tiene el 30 que m\u00e1s tienen<\/p>

# percentil 70<\/p>

qnorm(0.7, mean = 192, sd = 12)<\/p>

198.2928<\/p>

#### EJEMPLO 2<\/p>

# la edad de un grupo de personas sigue una N(35,10)<\/p>

# Calcula la prob de que una persona al azar tenga<\/p>

#A) M\u00e1s de 40 a\u00f1os — P x > 40<\/p>

# = 1- p(X<=40)<\/p>

1- pnorm(40,35,10)<\/p>

0.3085375<\/p>

#B)Entre 23 y 47 a\u00f1os. P(23< X < 47)<\/p>

# P[X \u2264 47] \u2013 P[ X \u226423]<\/p>

pnorm(c(47, 23), mean = 35, sd = 10)<\/p>

0.8849303 – 0.1150697<\/p>

0.7698606<\/p>

# C) Di entre qu\u00e9 edades estar\u00e1 comprendido el 50 % central de la distribuci\u00f3n<\/p>

qnorm(0.30, mean = 35, sd = 10)<\/p>

qnorm(0.70, mean = 35, sd = 10)<\/p>

#\u2666entre 28 a\u00f1os y 42<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

La Distribuci\u00f3n Normal\u200b es la m\u00e1s importante de las distribuciones continuas, debido a la gran cantidad de fen\u00f3menos reales en la que se usa. Esta distribuci\u00f3n tambi\u00e9n se conoce como gaussiana o de Gauss\u200b, en honor a su descubridor. SI nos fijamos en su forma cabe destacar que es sim\u00e9trica y tiene forma de campana. …<\/p>\n

Distribuci\u00f3n Normal en R<\/span> Leer m\u00e1s »<\/a><\/p>\n","protected":false},"author":1,"featured_media":2308,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[2],"tags":[],"yoast_head":"\nDistribuci\u00f3n Normal en R - V\u00edctor A. 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