Q:

When normal and poisson approximation is good/bad

Normal approximation and poisson approximation is used to approximate binomial distribution.
when these approximation are good? when bad?

A:

The Normal distribution is symmetric. The binomial distribution is symmetric only when the probability of success, usually denoted by $p$ is $\frac{1}{2}$. Thus if the departure of $p$ from $\frac{1}{2}$ is large, intuitively, it seems that it may not be good to use the normal approximation, which is the case if the number of trials $n$ is small. However, when $n$ is large, the Normal approximation stands solid by the very powerful Central limit theorem, which is basically the heart of Large sample theory.
On the other hand Poisson approximation is done by taking the parameter $\lambda$ to be equal to the product $n \times p$. It is good when $n$ is large, $p$ is small, but $n \times p$ is a finite quantity.Starting with the probability mass function of the Binomial distribution, taking the limits $n \to \infty$ and $p \to 0$, and putting $n \times p = \lambda$, one can get the probability mass function of the Poisson distribution. Obviously if these conditions (large $n$, small $p$ and finite $n \times p$) are violated, the Poisson approximation doesn't hold good.

