Percentage defect afval op een bepaalde dag

round((3000/627992),4)
## [1] 0.0048

Dat is ongeveer 5 promille

Berekening hoeveel sigma op een normaal verdeling (links en rechts 2.5 promille)

qnorm(3000/2/627992)
## [1] -2.82169

Controle door deze sigma’s in te vullen in pnorm.

round(pnorm(-2.82, mean=0, sd=1, lower.tail = TRUE)+
        pnorm(2.82, mean=0, sd=1, lower.tail = FALSE),4)
## [1] 0.0048

Dat is dus bijna 3 sigma

# Children's IQ scores are normally distributed with a
# mean of 100 and a standard deviation of 15. What
# proportion of children are expected to have an IQ between
# 80 and 120?

mean=0; sd=1
lb=-2.8; ub=2.8

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

plot(x, hx, type="n", xlab="DPMO", ylab="",
  main="Normal Distribution", axes=FALSE)

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

area <- pnorm(ub, mean, sd) - pnorm(lb, mean, sd)
result <- paste("P(",lb,"< defect <",ub,") =",
   signif(area, digits=3))
mtext(result,4)
axis(1, at=seq(-4, 4, 1), pos=0)