Exercicio

---

library(RcmdrMisc) 

## Warning: package 'RcmdrMisc' was built under R version 4.0.5

## Loading required package: car

## Warning: package 'car' was built under R version 4.0.3

## Loading required package: carData

## Warning: package 'carData' was built under R version 4.0.3

## Loading required package: sandwich

## Warning: package 'sandwich' was built under R version 4.0.5

P(0<X<0,11) = 0,04380

.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, 0.11)), 
          col=c('pink'), legend=FALSE)

P(-2,2<X<0,12)

P(-2,2 <z < 0,12) = P(-2,2 < z < 0) + P(0<z<0,12)

P(-2,2 <z < 0,12) = P(0 < z < 2,2) + P(0<z<0,12)

P(-2,2 <z < 0,12) = 0.48610 + 0.04776

P(-2,2 <z < 0,12) = 0.53386

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('pink','black'), legend=FALSE)

P(-1<X<2,1)

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

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

P(-1 <z < 2,1) = 0.34134 + 0.48214

P(-1 <z < 2,1) = 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('orange','black'), legend=FALSE)

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('blue'), legend=FALSE)

P(-0,87<X<1,54)

P(-0,87 <z < 1,54) = P(-0,87 < z < 0) + P(0<z<1,54)

P(-0,87 <z < 1,54) = P(0 < z < 0,87) + P(0<z<1,54)

P(-0,87 <z < 1,54) = 0.30785 + 0.43822

P(-0,87 <z < 1,54) = 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('purple','black'), legend=FALSE)

P(x>2,5)

plotDistr(.x, dnorm(.x, mean=0, sd=1), cdf=FALSE, xlab="z", 
          ylab="Densidade",regions=list(c(2.5,10)), 
          col=c('pink'), legend=FALSE)

P(x>-2)

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