# Problem:  Suppose a production process produces widgets with a weight distributed
# as a normal variable with mean of 100 grams and standard deviation of 10 grams.
# What is the probability of a random sample of size 25 having a mean value that is
# outside 100 +- 2 grams?

cord.x <- c(-3, seq(-3, -2*(5)/10, 0.01), -2*(5)/10)
cord.y <- c(0, dnorm(seq(-3, -2*(5)/10, 0.01),0,1), 0)
cord.xx <- c(2*(5)/10, seq(2*5/10, +3, 0.01), +3)
cord.yy <- c(0, dnorm(seq(2*5/10, +3, 0.01),0,1), 0)
curve(dnorm(x,0,1),xlim=c(-3,3),main="Standard Normal Density", ylab = "density")
polygon(cord.x,cord.y,col="skyblue")
polygon(cord.xx,cord.yy,col="skyblue")