x=seq(-3,3,length=200)

y=dnorm(x,mean=0,sd=1)

plot(x,y)

plot of chunk unnamed-chunk-1

plot(x,y,type="l")

plot of chunk unnamed-chunk-1

x=seq(20,80,length=200)

y=dnorm(x,mean=50,sd=10)

plot(x,y,type="l")

plot of chunk unnamed-chunk-1

x=seq(-3,3,length=200)

y=dnorm(x,mean=0,sd=1)

plot(x,y,type="l")

x=seq(-3,0,length=100)

y=dnorm(x,mean=0,sd=1)

polygon(c(-3,x,0),c(0,y,0),col="red")

plot of chunk unnamed-chunk-1

pnorm(0,mean=0,sd=1)
## [1] 0.5
x=seq(-3,3,length=200)

y=dnorm(x,mean=0,sd=1)

plot(x,y,type="l")

x=seq(-3,1,length=100)

y=dnorm(x,mean=0,sd=1)

polygon(c(-3,x,1),c(0,y,0),col="red")

plot of chunk unnamed-chunk-1

pnorm(1,mean=0,sd=1)
## [1] 0.8413
x=seq(-3,3,length=200)

y=dnorm(x,mean=0,sd=1)

plot(x,y,type="l")

x=seq(2,3,length=100)

y=dnorm(x,mean=0,sd=1)

polygon(c(2,x,3),c(0,y,0),col="red")

plot of chunk unnamed-chunk-1

1-pnorm(2,mean=0,sd=1)
## [1] 0.02275
x=seq(-3,3,length=200)

y=dnorm(x,mean=0,sd=1)

plot(x,y,type="l")

x=seq(-1,1,length=100)

y=dnorm(x,mean=0,sd=1)

polygon(c(-1,x,1),c(0,y,0),col="red")

plot of chunk unnamed-chunk-1

pnorm(1,mean=0,sd=1)-pnorm(-1,mean=0,sd=1)
## [1] 0.6827
x=seq(20,80,length=200)

y=dnorm(x,mean=50,sd=10)

plot(x,y,type="l")

x=seq(30,70,length=100)

y=dnorm(x,mean=50,sd=10)

polygon(c(30,x,70),c(0,y,0),col="red")

plot of chunk unnamed-chunk-1

pnorm(70,mean=50,sd=10)-pnorm(30,mean=50,sd=10)
## [1] 0.9545
x=seq(-3,3,length=200)

y=dnorm(x,mean=0,sd=1)

plot(x,y,type="l")

x=seq(-3,-0.2533,length=100)

y=dnorm(x,mean=0,sd=1)

polygon(c(-3,x,-0.2533),c(0,y,0),col="red")

text(-1,0.1,"0.40")

plot of chunk unnamed-chunk-1

qnorm(0.40,mean=0,sd=1)
## [1] -0.2533
x=seq(-3,3,length=200)

y=dnorm(x,mean=0,sd=1)

plot(x,y,type="l")

x=seq(-3,-0.2533,length=100)

y=dnorm(x,mean=0,sd=1)

polygon(c(-3,x,-0.2533),c(0,y,0),col="red")

text(-1,0.1,"0.40")

arrows(0.5,0.1,-0.2,0,length=.15)

text(0.5,0.12,"-0.2533")

plot of chunk unnamed-chunk-1

x=seq(-3,3,length=200)

y=dnorm(x,mean=0,sd=1)

plot(x,y,type="l")

x=seq(0.5244,3,length=100)

y=dnorm(x,mean=0,sd=1)

polygon(c(0.5244,x,3),c(0,y,0),col="red")

text(1,0.1,"0.30")

plot of chunk unnamed-chunk-1

qnorm(0.70,mean=0,sd=1)
## [1] 0.5244
x=seq(-3,3,length=200)

y=dnorm(x,mean=0,sd=1)

plot(x,y,type="l")

x=seq(0.5244,3,length=100)

y=dnorm(x,mean=0,sd=1)

polygon(c(0.5244,x,3),c(0,y,0),col="red")

text(1,0.1,"0.30")

arrows(-0.5,0.1,0.45,0,length=.15)

text(-0.5,0.12,"0.5244")

plot of chunk unnamed-chunk-1

x=seq(15,105,length=200)

y=dnorm(x,mean=60,sd=15)

plot(x,y,type="l",xaxt="n")

axis(1,at=c(15,30,45,60,75,90,105))

plot of chunk unnamed-chunk-1

x=seq(15,105,length=200)

y=dnorm(x,mean=60,sd=15)

plot(x,y,type="l",xaxt="n")

axis(1,at=c(15,30,45,60,75,90,105))

x=seq(72.62,105,length=100)

y=dnorm(x,mean=60,sd=15)

polygon(c(72.62,x,105),c(0,y,0),col="red")

text(80,0.005,"0.20")

plot of chunk unnamed-chunk-1

qnorm(0.80,mean=60,sd=15)
## [1] 72.62
x=seq(15,105,length=200)

y=dnorm(x,mean=60,sd=15)

plot(x,y,type="l",xaxt="n")

axis(1,at=c(15,30,45,60,75,90,105))

x=seq(72.62,105,length=100)

y=dnorm(x,mean=60,sd=15)

polygon(c(72.62,x,105),c(0,y,0),col="red")

text(80,0.005,"0.20")

arrows(60,0.004,71.5,0,length=.15)

text(60,0.0055,"72.62")

plot of chunk unnamed-chunk-1