# Approximation of “translated and scaled” Poisson distribution by normal distribution?

If I have a random variable $Y=a(\frac{b}{c}+\frac{X}{c})$, where $a,b,c$ are all integers and $X$ is Poisson distributed with a mean which is large enough to be approximated by the normal distribution. Can $Y$ then be approximated by a normal distribution as well?

• Yes. Why would you think otherwise? – Hong Ooi Feb 6 '15 at 13:37

Your formulation is equivalent to $Y=a_1X+b_1$; you don't really need three coefficients to achieve translation and scaling. This is more general than your formulation (because my $a_1$ and $b_1$ are not restricted to integer multiples of $1/c$ for $c$ integer) but the answer applies more generally.