This is part of the HSC Mathematics Extension 1 course under the topic: The Binomial Distribution.

In this post, we learn about what a sample proportion is and how it can be modelled after the normal approximation.

##### Some definitions:

**Sample proportion:**the number of favourable outcomes/successes**Sampling distribution:**probability distribution made from a larger number of samples.number of successes in n repeated trials of a*Binomial*random variable:*binomial*experiment.**Binomial distribution:**is the statistical distribution modelling the outcomes of two complementary events (like flipping a coin, i.e. only one even or the other can occour).

A binomial distribution has 3 main characteristics

- n the number of trials
- p the probability of success
- 1-p the probability of failure.

However, when n gets too large (typically above 40), it’s better to model the distribution using a normal approximation or normal distribution, as described in the following videos.

### Sampling distributions

Here are some videos so we can gain a deeper explanation and some examples of using the idea of normal approximation for sample proportions.

Finally, let’s explore how we can use normal approximations for large samples.