Atividade 7 - Distribuição Normal

Carregamento de pacote

library(RcmdrMisc)

## Carregando pacotes exigidos: car

## Carregando pacotes exigidos: carData

## Carregando pacotes exigidos: sandwich

1: P (x < 0) = 0.5

.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('darkred'), legend=FALSE)

2: P( 0 < x < 0.11) = 0.04380

plotDistr(.x, dnorm(.x, mean=0, sd=1), cdf=FALSE, xlab="n", ylab="Densidade",
          regions=list(c(0, 0.11)), col=c('green', '#BEBEBE'), legend=FALSE)

3: P(-2.2 < x < 0.12) = P(-2,2 < x < 0) + P(0 < x < 0,12) = 0.4783 + 0.04776 = 0.52606

plotDistr(.x, dnorm(.x, mean=0, sd=1), cdf=FALSE, xlab="z", 
          ylab="Densidade",regions=list(c(-2.2,0),c(0,0.12)), 
          col=c('red', 'blue'), legend=FALSE)

4: P(-1 < x < 2.1) = P(-1 < x < 0) + P(0 < x < 2.1) = 0.34134 + 0.48214 = 0.82348

plotDistr(.x, dnorm(.x, mean=0, sd=1), cdf=FALSE, xlab="z", 
          ylab="Densidade",regions=list(c(-1,0),c(0,2.1)), 
          col=c('green','red'), legend=FALSE)

5: P(0 < x < 1.83) = 0.46638

plotDistr(.x, dnorm(.x, mean=0, sd=1), cdf=FALSE, xlab="z", 
          ylab="Densidade",regions=list(c(0,1.83)), 
          col=c('purple'), legend=FALSE)

6: P(-0.87 < x 1.54) = P (-0.87 < x < 0) + P(0 < x < 1.54) = 0.30785 + 0.43822 = 0.74607

plotDistr(.x, dnorm(.x, mean=0, sd=1), cdf=FALSE, xlab="z", 
          ylab="Densidade",regions=list(c(-0.87,0),c(0,1.54)), 
          col=c('green','pink'), legend=FALSE)

7: P(X = 1,54) = 0

Essa questão é considerada nula pela área calculada ser inválida.

8: P(X > 2.5) = 0.5 - 0.4937 = 0.0063

plotDistr(.x, dnorm(.x, mean=0, sd=1), cdf=FALSE, xlab="z", 
          ylab="Densidade",regions=list(c(2.5,4)), 
          col=c('red'), legend=FALSE)

9: P(X > -2) = 0.4772 + 0.5 = 0.9772

plotDistr(.x, dnorm(.x, mean=0, sd=1), cdf=FALSE, xlab="x", ylab="Densidade",
          regions=list(c(-2, 10)), col=c('pink', '#BEBEBE'), legend=FALSE)