Let X ~ Binom(n, pi). Then by the Central Limit Theorem, if n is large enough, X is approximately equal to Norm(pi, sqrt(npi(1 - pi))). I need to show that if pi > .5 and npi >= 10, then 3sqrt(pi(1-pi)/n) < pi.

What i tried was rewriting n as n >= 10/pi, and then plugging this in to the left half of the expression. I got it reduced to 3sqrt((1-pi)/10) < 1, but I am not sure where to go from there.

Or maybe there is some other way to do this that I am not thinking of.