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.
- Sample proportion: the number of favourable outcomes/successes
- Sampling distribution: probability distribution made from a larger number of samples.
- Binomial random variable: number of successes in n repeated trials of a 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.
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.