n = 20
k = 2

M = NULL

## Consider different success probabilities.
for (p in c(0.01, 0.1, 0.2, 0.3, 0.4, 0.5))
{
  ## The probability from the normal approximation.
  N = 1 - pnorm((k-n*p)/sqrt(n*p*(1-p)))

  ## The probability from the Poisson approximation.
  P = 1 - ppois(k, n*p)

  ## The exact value from the binomial distribution.
  B = 1 - pbinom(k, n, p)

  M = rbind(M, c(p, B, N, P, (N-B)/B, (P-B)/B))
}

print(round(M, 3))