m = 100000
#number of samples

n = 10
#size of a sample

mu = 5
#expectation

var = 4
#variance

A = matrix( rnorm(n*m,mean=mu,sd=sqrt(var)), m, n)
#generate a vector of n*m random variable with mean mu e variance var and trasnform it in a matrix m by n

avg = rowMeans(A)
#compute the average of each sample

sum(abs(avg-mu)<=sqrt(var/10)*1.96)
#count how many times the expercation falls in the confidence interval