Carregando a biblioteca

library(RcmdrMisc)
## Loading required package: car
## Loading required package: carData
## Loading required package: sandwich

IntroduĆ§Ć£o a curva normal

x <- seq(-3.3, 3.3, length.out=1000) 


plotDistr(x, dnorm(x, mean=0, sd=1), cdf=FALSE, xlab="x", ylab="Densidade",
          regions=list(c(-1, 1)), col=c('#0080C0'), legend=FALSE)

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

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

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

Regra da normal

# regra da normal = 68%, 95.4%, 99.7%



# P(0<x<1) = 0.34
  
  
  
plotDistr(x, dnorm(x, mean=0, sd=1), cdf=FALSE, xlab="x", ylab="Densidade",
            regions=list(c(0, 1)), col=c('yellow'), legend=FALSE)

# P(-2<X<0) = 0.475
    
    
plotDistr(x, dnorm(x, mean=0, sd=1), cdf=FALSE, xlab="x", ylab="Densidade",
              regions=list(c(-2, 0)), col=c('yellow'), legend=FALSE)

# P(0<X<3) = 0.4985  
  

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

# x ~ N(0,1)

# P(1<X<3) = P(0<X<3) - P(0<X<1) = 0.4985 - 0.34 = 0.1585


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

# x ~ N(0,1)

# P(2<X<3) = P(0<X<3) - P(0<X<2) =  0.4985 - 0,475 = 0.0235


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

# P(-1<X<2) = P(-1<X<0) + P(0<X<2) = 0.34 + 0.475 = 0.815


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

# P(-2<X<3) = P(-2<X<0) + P(0<X<3) = 0.4985 + 0,475 = 0.9735

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

# P(X<2) =


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

# P(X<2) = P(0<X<INFINITO) + P(0<X<2) = 0.5 - 0.475 = 0.025

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

# P(X<-2) = P(0<X<INFINITO) + P(0<X<2) = 0.5 + 0.475 = 0.975

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

Tabela da normal

# P(0<X<1.34) = 0.40988
# P(0<X<0.29) = 0.11409

# P(0<X<2.03) = 0.47882

# P(0<X<1.27) = 0.37900

# P(-1.14<X<0) = 0.37286

# P(0.23<X<0.29) = 0,20504

Usando o R para calcular

pnorm(0.29) -pnorm(-0.23)
## [1] 0.205046
# P(1.11<X<2.14) = 0.1173221
pnorm(2.14) -pnorm(1.11)
## [1] 0.1173221
u=seq(0,3.09,by=0.01)  
p=pnorm(u)  
p=p-0.5  
m=matrix(p,ncol=10,byrow=TRUE)  
m=round(m,4)  
DT::datatable(m)