Thread: normal approximation for discrete random variables

If it can be done, what are the minimum conditions for a normal approximation to be valid for discrete random variables. I know it can be done for a binomial if np and nq are larger than 10, but what about a case with not just simply success or failures?

For example,

x p(x)
0 0.2
1 0.3
2 0.5

mean is 1.3 and variance 0.61

if x is chosen 100 times could the total of x, lets call it Y, use normal approximation where Y ~N(100*1.3,sqrt(100*0.61)) ???

Cheers

Hello,

See how the central limit theorem is stated. It should be a normal approximation of 10*(Y/100 - 1.3) to N(0, 0.61)