Let $X$ be binomially distributed with parameters $n$ and $p$, i.e. $X \sim Bin(n,p), q := 1- p \in (0,1)$
$a)$ $X$ represents the number of white balls when taking $n $ balls out of an urn without putting them back with $w$ balls being white and $p = w/n$.
$b)$ $X$ is approximately normally distributed when $p$ is small.
$c)$ $E(X) = np$
$d)$ $X$ does not have a variance
$e)$ $X$ is approximately Poisson-distributed, when $n$ and $q$ are big
We have the following answers, but we are unsure, if these are correct:
$a)$ False because we can't put the balls back into the urn
$b)$ False. It's only true when $p$ is big
$c)$ True
$d)$ False (because every distribution has variance)
$e)$ True (because poission is strictly positive)
Any correction or help is appreciated!
(e) is true because Poisson is a good approximation to Binomial when $n$ is large and $p$ is small. The question says $q$ is large, ie. $p=1-q$ is small. So that's why (e) is true. http://bestmaths.net/online/index.php/year-levels/year-12/year-12-topic-list/poisson-approximation-binomial/
Other than that, your answers seem correct to me.