Assignment 16 qs

x=seq(40,160,length=200)
y=dnorm(x,mean=100,sd=20)

plot(x,y)

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

x=seq(40,100,length=100)

y=dnorm(x,mean=100,sd=20)

polygon(c(40,x,100),c(100,y,100),col="red")

pnorm(110,mean=100,sd=20)

## [1] 0.6915

x=seq(20,80,length=200)
y=dnorm(x,mean=50,sd=10)

plot(x,y)

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

x=seq(20,50,length=100)

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

polygon(c(20,x,50),c(50,y,50),col="blue")

1-pnorm(40,mean=50,sd=10)

## [1] 0.8413

x=seq(25,115,length=200)
y=dnorm(x,mean=70,sd=15)

plot(x,y)

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

x=seq(25,70,length=100)

y=dnorm(x,mean=70,sd=15)

polygon(c(25,x,70),c(70,y,70),col="green")

pnorm(85,mean=70,sd=15)-pnorm(60,mean=70,sd=15)

## [1] 0.5889

x=seq(25,55,length=200)
y=dnorm(x,mean=40,sd=5)

plot(x,y)

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

x=seq(25,40,length=100)

y=dnorm(x,mean=40,sd=5)

polygon(c(25,x,40),c(40,y,40),col="yellow")

pnorm(38.78,mean=40,sd=5)

## [1] 0.4036

x=seq(2,38,length=200)
y=dnorm(x,mean=20,sd=6)

plot(x,y)

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

x=seq(2,20,length=100)

y=dnorm(x,mean=20,sd=6)

polygon(c(2,x,20),c(20,y,20),col="violetred")

1-pnorm(15.9,mean=20,sd=6)

## [1] 0.7528

The Minimal score one must get is 89.99% in order to be in the top 15% of the class and receive an “A”

x=seq(50,110,length=200)
y=dnorm(x,mean=80,sd=10)

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

x=seq(50,80,length=100)

y=dnorm(x,mean=80,sd=10)

polygon(c(50,x,80),c(80,y,80),col="purple")

1-pnorm(89.99,mean=80,sd=10)

## [1] 0.1589