IS pi a probability?
and the mean of a binomial is n times the probability.
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.
The second parameter in (which is the usual notation for the normal distribution) is usually the variance not the standard deviation.
So you want to show that: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.
or:
So we start:
etc
How did you get to this step?