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library(RcmdrMisc)  
## Warning: package 'RcmdrMisc' was built under R version 4.2.2
## Carregando pacotes exigidos: car
## Warning: package 'car' was built under R version 4.2.2
## Carregando pacotes exigidos: carData
## Warning: package 'carData' was built under R version 4.2.2
## Carregando pacotes exigidos: sandwich
## Warning: package 'sandwich' was built under R version 4.2.2
x = seq(-3.291, 3.291, length.out=1000)

Z ~ N(0,1) Pr(-1<Z<2,1) = 0.8234803 = 82.35%

plotDistr(x, dnorm(x, mean=0, sd=1), cdf=FALSE, 
          regions=list(c(-1, 2.1)), col=c("#0abab9"),
          legend=FALSE)

Pr(-0,87<Z<1,54) = 0.7460696 = 74.61%

plotDistr(x, dnorm(x, mean=0, sd=1), cdf=FALSE, 
          regions=list(c(-0.87, 1.54)), col=c("#0abab9"),
          legend=FALSE)

X ~ N(500,300) Pr(400<X<710) = Pr((400-500)/300<Z<((710-500)/300) = Pr(-0.33<Z<0.7) = 0.3873364 = 38.73%

plotDistr(x, dnorm(x, mean=0, sd=1), cdf=FALSE, 
          regions=list(c(-0.33, 0.7)), col=c("#0abab9"),
          legend=FALSE)

Pr(330<X<450) = Pr((330-500)/300<Z<((450-500)/300) = Pr(-0.57<Z<-0.17) = 0.1481662 = 14.82%

plotDistr(x, dnorm(x, mean=0, sd=1), cdf=FALSE, 
          regions=list(c(-0.57, -0.17)), col=c("#0abab9"),
          legend=FALSE)

Y ~ N(100,20) Pr(50<Y<70) = Pr((50-100)/20<Z<((70-100)/20) = Pr(-2.5<Z<-1.5) = 0.06059754 = 6.06%

plotDistr(x, dnorm(x, mean=0, sd=1), cdf=FALSE, 
          regions=list(c(-2.5, -1.5)), col=c("#0abab9"),
          legend=FALSE)

Pr(105<Y<110) = Pr((105-100)/20<Z<((110-100)/20) = Pr(0.25<Z<0.50) = 0.09275614 = 9.28%

plotDistr(x, dnorm(x, mean=0, sd=1), cdf=FALSE, 
          regions=list(c(0.25, 0.50)), col=c("#0abab9"),
          legend=FALSE)