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title: “Dist normal” author: “Alejandro Medrano” date: “19/6/2020” output: html_document —Objetivo Realizar algunos cálculos de probabilidad haciendo uso de la Distribución Normal Estándard y mediante la función dnorm() Las librerías

library(mosaic)

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library(dplyr)

1. Encontar la probabildiad para cuando p(z≤1) con μ=0 y σ=1. Se usa pnorm() para encontrar probabilidad acumulada

pnorm(1, mean = 0, sd= 1)

## [1] 0.8413447

Visualizar la distribución de probabilidad normal estándard para cuando μ=0 y σ=1

plotDist("norm", mean = 0, sd = 1, groups = x < 1, type = "h")

2. Encontar la probabilidad para cuando p(−0.50≤x≤1.25) con μ=0 y σ=1. Se usa pnorm() para encontrar probabilidad acumulada y restando p(1.25)−p(−0.50)

pnorm(1.25, mean = 0, sd= 1) -pnorm(-0.50, mean = 0, sd= 1)

## [1] 0.5858127

####Visualizar la distribución de probabilidad normal estándard para cuando μ=0 y σ=1

plotDist("norm", mean = 0, sd = 1, groups = x > -0.50 & x < 1.25, type = "h")

3. Encontar la probabilidad para cuando p(z≥1.58) con μ=0 y σ=1. Se usa pnorm() para encontrar probabilidad acumulada y restando p(x>1.58)=1−p(x≤1.58)

1 - pnorm(c(1.58), mean = 0, sd= 1)

## [1] 0.05705343

pnorm(c(1.58), mean = 0, sd= 1, lower.tail= F)

## [1] 0.05705343

Visualizar la distribución de probabilidad normal estándard para cuando μ=0 y σ=1

plotDist("norm", mean = 0, sd = 1, groups = x > 1.58, type ="h")

Distribución de Probabilidad Normal 1.Para cuando cuando media es diferente de cero 2.Desviación estándard es diferente de 1 Realizar estos ejemplos: … Calcular probabilidades en cualquier distribucion normal, se tiene una distribución en la que: μ=10 y σ=2 ¿Cual es la probabilidad de que la variable aleatoria x este entre 10 y 14?

#primero convertir y luego
pnorm(2, mean=0, sd=1)-pnorm(0, mean=0, sd=1)

## [1] 0.4772499

pnorm(14, mean=10, sd=2)-pnorm(10, mean=10, sd=2)

## [1] 0.4772499

Visualizar la distribución de probabilidad normal estándard para cuando μ=10 y σ=2

plotDist("norm", mean = 10, sd = 2, groups = x > 10 & x < 14, type ="h")

pnorm(14, mean = 10, sd = 2) - pnorm(10, mean = 10, sd = 2)

## [1] 0.4772499

¿Cual es la probabilidad de que sea mayor que 12?

plotDist("norm", mean = 10, sd = 2, groups = x > 12, type ="h")

Opción 1

1 - pnorm(q=12, mean = 10, sd = 2)

## [1] 0.1586553

Opcion 2

pnorm(q=12, mean = 10, sd = 2, lower.tail = FALSE)

## [1] 0.1586553