Exercícios de Distribuição Normal

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('royalblue', '#BEBEBE'), legend=FALSE)

1. P (X < 0) = 0,5

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

2. P (0 < X < 0,11) = 0.04380

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

3. (-2.2 < 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(-2.2,0.12)),
          col=c('royalblue'),
          legend=FALSE)

4. (-1 < X < 2.1) = 0.3413 + 0.4821 = 0.8234

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

5. (0 < X < 1.83) = 0.4663

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

6. (-0.87 < X < 1.54) = 0.4382 + 0.3078 = 0.7460

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

7. Com relação a (X = 1,54) será igual a 0 (zero), pois estaremos calculando a área de uma linha, cujo resultado é sempre zero.

8. (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, 10)),
          col=c('royalblue'),
          legend=FALSE)

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

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