a little adjustment.

# LLN

epsilon = 0.1

m = 100       # repetition to get the probability
n = 1000

percent = 1:n
index = 1:n   # the number of r.s. to get xbar

for (i in 1:n){
  Count = 0
  for (j in 1:m){
     z = rnorm(i)
     y = mean(z)
     if (abs(y) > epsilon) Count = Count + 1
  }
  percent[i] = Count/m
}

plot(index, percent, type='p', main = 'Approximate Probability of exceeding epsilon')

percent[n]