SA UPEŠ Vaje2 Naloga2

#VPRAŠANJE a
#Določimo normalno porazdelitev in izračunamo iskano ploščino
pnorm(117, mean=100, sd=17, lower.tail=TRUE) 

## [1] 0.8413447

#Ukaz za risanje gostote verjetnosti za normalno porazdelitev. Spreminjamo samo mean, sd, lb in ub.
mean=100; sd=17
lb=-Inf; ub=117

x <- seq(-4,4,length=100)*sd + mean
hx <- dnorm(x,mean,sd)

plot(x, hx, type="n", xlab="IQ", ylab="",
  main="", axes=FALSE)

i <- x >= lb & x <= ub
lines(x, hx)
polygon(c(lb,x[i],ub), c(0,hx[i],0), col="blue") 

area <- pnorm(ub, mean, sd) - pnorm(lb, mean, sd)
result <- paste("P(",lb,"< IQ <",ub,") =",
   signif(area, digits=3))
mtext(result,3)
axis(1, at=seq(40, 160, 20), pos=0)

#VPRAŠANJE b
#Določimo normalno porazdelitev in izračunamo iskano ploščino
a<-pnorm(91.5, mean=100, sd=17, lower.tail=TRUE)
b<-pnorm(108.5, mean=100, sd=17, lower.tail=TRUE)
a

## [1] 0.3085375

b

## [1] 0.6914625

Ploščina = b-a
Ploščina

## [1] 0.3829249

mean=100; sd=17
lb=91.5; ub=108.5

x <- seq(-4,4,length=100)*sd + mean
hx <- dnorm(x,mean,sd)

plot(x, hx, type="n", xlab="IQ", ylab="",
  main="", axes=FALSE)

i <- x >= lb & x <= ub
lines(x, hx)
polygon(c(lb,x[i],ub), c(0,hx[i],0), col="blue") 

area <- pnorm(ub, mean, sd) - pnorm(lb, mean, sd)
result <- paste("P(",lb,"< IQ <",ub,") =",
   signif(area, digits=3))
mtext(result,3)
axis(1, at=seq(40, 160, 20), pos=0)

#Vprašanje c
pnorm(154, mean=100, sd=17, lower.tail=FALSE) 

## [1] 0.0007453945

mean=100; sd=17
lb=154; ub=Inf

x <- seq(-4,4,length=100)*sd + mean
hx <- dnorm(x,mean,sd)

plot(x, hx, type="n", xlab="IQ", ylab="",
  main="", axes=FALSE)

i <- x >= lb & x <= ub
lines(x, hx)
polygon(c(lb,x[i],ub), c(0,hx[i],0), col="blue") 

area <- pnorm(ub, mean, sd) - pnorm(lb, mean, sd)
result <- paste("P(",lb,"< IQ <",ub,") =",
   signif(area, digits=3))
mtext(result,3)
axis(1, at=seq(40, 160, 20), pos=0)

#Vprašanje D
z<-qnorm(0.90)
z

## [1] 1.281552

y = mean + z * sd
y

## [1] 121.7864