Aula 8 Estatística

Normal padrão

Z - N(0,1)

library(RcmdrMisc)  

## Carregando pacotes exigidos: car

## Carregando pacotes exigidos: carData

## Carregando pacotes exigidos: sandwich

.x <- seq(-3.291, 3.291, length.out=1000)    
plotDistr(.x, dnorm(.x, mean=0, sd=1),
          cdf=FALSE, xlab="z", ylab="Densidade",regions=list(c(0, 4)),
          col=c('#0080C0', '#BEBEBE'), legend=FALSE)

P(-1 < z < 1) = 0,6826

plotDistr(.x, dnorm(.x, mean=0, sd=1),
          cdf=FALSE, xlab="z", ylab="Densidade",regions=list(c(-1, 1)),
          col=c('red'), legend=FALSE)

P(-2 < z < 2) = 0,9544

plotDistr(.x, dnorm(.x, mean=0, sd=1),
          cdf=FALSE, xlab="z", ylab="Densidade",regions=list(c(-2, 2)),
          col=c('green'), legend=FALSE)

P(-3 < z < 3) = 0,9974

plotDistr(.x, dnorm(.x, mean=0, sd=1),
          cdf=FALSE, xlab="z", ylab="Densidade",regions=list(c(-3, 3)),
          col=c('yellow'), legend=FALSE)

P(0 < z < 1) = 0,6826/2

P(0 < z < 1) = 0,3413

plotDistr(.x, dnorm(.x, mean=0, sd=1),
          cdf=FALSE, xlab="z", ylab="Densidade",regions=list(c(0, 1)),
          col=c('skyblue'), legend=FALSE)

P(0 < z < 2) = 0,9544/2 = 0,4772

plotDistr(.x, dnorm(.x, mean=0, sd=1),
          cdf=FALSE, xlab="z", ylab="Densidade",regions=list(c(0, 2)),
          col=c('darkblue'), legend=FALSE)

P(-3 < z < 0) = P(0 < z < 3) = 0,9974/2 = 0,4987

plotDistr(.x, dnorm(.x, mean=0, sd=1),
          cdf=FALSE, xlab="z", ylab="Densidade",regions=list(c(-3, 0),c(0,3)),
          col=c('purple','gold'), legend=FALSE)

P(-2 < z < 0) = P(0 < z < 2) = 0,4772

plotDistr(.x, dnorm(.x, mean=0, sd=1),
          cdf=FALSE, xlab="z", ylab="Densidade",regions=list(c(-2, 0),c(0,2)),
          col=c('orange','brown'), legend=FALSE)

P( 1 < Z < 2) = P(0 < Z < 2) - P(0 < Z < 1) = 0,4772 - 0,3413

P( 1 < Z < 2) = 0, 1359

plotDistr(.x, dnorm(.x, mean=0, sd=1),
          cdf=FALSE, xlab="z", ylab="Densidade",regions=list(c(1, 2)),
          col=c('darkgreen'), legend=FALSE)

plotDistr(.x, dnorm(.x, mean=0, sd=1),
          cdf=FALSE, xlab="z", ylab="Densidade",regions=list(c(0,1),c(1,2)),
          col=c('pink','darkgreen'), legend=FALSE)

P(2 < Z < 3) = P(0 < Z < 3) - P(0 < Z < 2) = 0,4987 - 0,4772

P(2 < Z < 3) = 0,0215

plotDistr(.x, dnorm(.x, mean=0, sd=1),
          cdf=FALSE, xlab="z", ylab="Densidade",regions=list(c(2, 3)),
          col=c('black'), legend=FALSE)

plotDistr(.x, dnorm(.x, mean=0, sd=1),
          cdf=FALSE, xlab="z", ylab="Densidade",regions=list(c(0,2),c(2,3)),
          col=c('gray','black'), legend=FALSE)

P(-3 < Z < 2) = P(-3 < Z < 0) + P(0 < Z < 2) = 0,4987 + 0,4772

P(-3 < Z < 2) = 0,9759

plotDistr(.x, dnorm(.x, mean=0, sd=1),
          cdf=FALSE, xlab="z", ylab="Densidade",regions=list(c(-3, 2)),
          col=c('royalblue'), legend=FALSE)

plotDistr(.x, dnorm(.x, mean=0, sd=1),
          cdf=FALSE, xlab="z", ylab="Densidade",regions=list(c(-3,0),c(0,2)),
          col=c('darkblue','skyblue'), legend=FALSE)

P(-2 < z < 1) = P(-2 < Z < 0) + P(0 < Z < 1) = 0,4772 + 0,3413

P(-2 < z < 1) = 0,8185

plotDistr(.x, dnorm(.x, mean=0, sd=1),
          cdf=FALSE, xlab="z", ylab="Densidade",regions=list(c(-2,0),c(0,1)),
          col=c('darkgreen','yellow4'), legend=FALSE)

(TABELA DA DISTRIBUIÇÃO NORMAL PADRÃO)

P(0 < z < 1,34) = 0,40988

plotDistr(.x, dnorm(.x, mean=0, sd=1),
          cdf=FALSE, xlab="z", ylab="Densidade",regions=list(c(0,1.34)),
          col=c('tomato'), legend=FALSE)

P(0 < z < 2,13) = 0,48341

plotDistr(.x, dnorm(.x, mean=0, sd=1),
          cdf=FALSE, xlab="z", ylab="Densidade",regions=list(c(0,2.13)),
          col=c('tomato4'), legend=FALSE)

P(-2,01 < Z < 1,17) = P(-2,01 < Z < 0) + P(0 < Z < 1,17) = 0,47778 + 0,37900

P(-2,01 < Z < 1,17) = 0.85678

plotDistr(.x, dnorm(.x, mean=0, sd=1),
          cdf=FALSE, xlab="z", ylab="Densidade",
          regions=list(c(-2.01,0),c(0,1.17)),
          col=c('orange1','pink4'), legend=FALSE)