Atividade 8

Atividade 8: Distribuição na Normal

library(RcmdrMisc) 

Z ~ N(0,1)

Pr(-1<Z<2,1) = 0.8234

Pr (-1-0/1) < (x-u/o) < (2,1-0/1)

Pr (-1 < z < 2,1)

x = seq(-3.291, 3.291, length.out=1000)  
plotDistr(x, dnorm(x, mean=0, sd=1), cdf=FALSE, 
          regions=list(c(-1,0), c(0,2.1)), col=c('purple','green'),
          legend=FALSE)

pnorm(2.1) - pnorm(-1)

## [1] 0.8234803

Pr(-0,87<Z<1,54) = 0.1303

Pr (-0,87-0/1) < (x-u/o) < (1,54-0/1)

Pr (-0,87 < z < 1,54)

x = seq(-3.291, 3.291, length.out=1000)  
plotDistr(x, dnorm(x, mean=0, sd=1), cdf=FALSE, 
          regions=list(c(-0.87,0), c(0,1.54)), col=c('purple','green'),
          legend=FALSE)

pnorm(1.54) - pnorm(-0.87)

## [1] 0.7460696

Pr(Z=1,54)

Pr(1,54-0/1) = 0.9382

x = seq(-3.291, 3.291, length.out=1000)  
plotDistr(x, dnorm(x, mean=0, sd=1), cdf=FALSE, 
          regions=list(c(0,1.54)), col=c('purple'),
          legend=FALSE)

pnorm(1.54)

## [1] 0.9382198

Pr(Z>2,5)

Pr(x-0/1) > (2,5-0/1) = 0.9973

x = seq(-3.291, 3.291, length.out=1000)  
plotDistr(x, dnorm(x, mean=0, sd=1), cdf=FALSE, 
          regions=list(c(2.5,3)), col=c('green'),
          legend=FALSE)

pnorm(3) - pnorm(2,5)

## [1] 0.9973002

X ~ N(500,300)

Pr(X<500)

Pr(x-500/300) < (500-500/300) =

x = seq(-3.291, 3.291, length.out=1000)  
plotDistr(x, dnorm(x, mean=0, sd=1), cdf=FALSE, 
          regions=list(c(0,500)), col=c('green'),
          legend=FALSE)

pnorm(3) 

## [1] 0.9986501

Pr(400<X<710) = 0.3873

Pr(400-500/300) < (x-u/o) < (710-500/300)

Pr(-100/300 < x < 210/300)

Pr(-0.33) < x < (0.7)

x = seq(-3.291, 3.291, length.out=1000)  
plotDistr(x, dnorm(x, mean=0, sd=1), cdf=FALSE, 
          regions=list(c(-0.33,0), c(0,0.7)), col=c('purple','green'),
          legend=FALSE)

pnorm(0.7) - pnorm(-0.33)

## [1] 0.3873364

Pr(330<X<450) = 0.1487

Pr(330-500/300) < x < (450-500/300)

Pr(330-500/300) < x < (450-500/300)

Pr(-170/300) < x < (-50/300)

Pr (-0.16) < x < (-0.56)

x = seq(-3.291, 3.291, length.out=1000)  
plotDistr(x, dnorm(x, mean=0, sd=1), cdf=FALSE, 
          regions=list(c(-0.56,0), c(-0.16,0)), col=c('purple','green'),
          legend=FALSE)

pnorm(-0.56) - pnorm(-0.16)

## [1] -0.1487008

Y ~ N(100,20)

Pr(50<Y<70) = -0.0605

Pr(50-100/20) < y < (70-100/20)

Pr(-50/20) < y < (-30/20)

Pr(-2,5) < y < (-1.5)

x = seq(-3.291, 3.291, length.out=1000)  
plotDistr(x, dnorm(x, mean=0, sd=1), cdf=FALSE, 
          regions=list(c(-2.5,0), c(-1.5,0)), col=c('purple','green'),
          legend=FALSE)

pnorm(-2.5) - pnorm(-1.5)

## [1] -0.06059754

Pr(105<Y<110) = 0.0927

Pr(105-100/20) < y < (110-100/20)

Pr(5/20) < y < (10/20)

Pr(0.25) < y < (0.5)

x = seq(-3.291, 3.291, length.out=1000)  
plotDistr(x, dnorm(x, mean=0, sd=1), cdf=FALSE, 
          regions=list(c(0, 0.5), c(0, 0.25)), col=c('purple','green'),
          legend=FALSE)

pnorm(0.5) - pnorm(0.25)

## [1] 0.09275614

Pr(Y>75) = 0.8930

Pr(y > 75-100/20)

Pr(y > -25/20)

Pr(y > -1.25)

x = seq(-3.291, 3.291, length.out=1000)  
plotDistr(x, dnorm(x, mean=0, sd=1), cdf=FALSE, 
          regions=list(c(-1.25, 3)), col=c('purple','green'),
          legend=FALSE)

pnorm(3) - pnorm(-1.25)

## [1] 0.8930003