Why Central limit theorem is not giving the correct Level of significance?
Graphical comment on the poor normal approximation for $\mathsf{Binom}(n-100,p=.05).$ [Using R to make graph.]
R code to make figure:
x = 0:20
bin.pdf = dbinom(x, 100, .05)
mu = 100*.05; mu
[1] 5
sg = sqrt(100*.05*.95): sg
[1] 2.179449
x = 0:20
bin.pdf = dbinom(x, 100, .05)
hdr = "Comparing PDF BINOM(100, .05) with NORM(5, 2.18)"
plot(x, bin.pdf, type="h", lwd=2, main=hdr)
abline(h=0, col="green2")
abline(v=0, col="green2")
curve(dnorm(x, 5, 2.18), add=T, col="blue", lwd=2)