set.seed(12345)

n<-10000;

z<-rnorm(n,0,1)
z1<-rnorm(n,0,1)
z2<-rnorm(n,0,1)
z3<-rnorm(n,0,1)
z4<-rnorm(n,0,1)
z5<-rnorm(n,0,1)

chi5<-z1^2+z2^2+z3^2+z4^2+z5^2

sqchi5<-sqrt(chi5/5)

t5<-z/sqchi5

hist(t5, breaks=100)