Why we need a t distribution

What does the following R code accomplish? How does it relate to the relevance of the t distribution?

x <- rnorm(60000,mean=355,sd=2)
data <- matrix(x,ncol=6)
xbar <- apply(data,1,mean)
s <- apply(data,1,sd)
z.ratio <- (xbar-355)/(2 / sqrt(6))
t.ratio <- (xbar-355)/(s/sqrt(6))

Now graph z.ratio and t.ratio using histograms with superimposed standard normal curves.

par(mfrow=c(2,1))
x <- seq(-4,4,len=201)
y <- dnorm(x)
hist(z.ratio,prob=T,xlim=c(-4,4),ylim=c(0,.4))
lines(x,y,type='l')
hist(t.ratio,prob=T,xlim=c(-4,4),ylim=c(0,.4))
lines(x,y,type='l')
par(mfrow=c(1,1))

R note: A better "goodness of normal fit" graphic than superimposing a normal onto a histogram is to use the qqnorm and its companion qqline functions. The closer to straight the plot, the more normal the data. Here is the syntax:

par(mfrow=c(2,1))
qqnorm(z.ratio)   # Is it straight?
qqline(z.ratio)   # Adding a line helps us decide.
qqnorm(t.ratio)
qqline(t.ratio)
par(mfrow=c(1,1))
# End of code