HSC Together Year 12 Maths Extension 1: Normal Approximation for the Sample Proportion

#### Maths Extension 1

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# Normal Approximation for the Sample Proportion

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.
• 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.

### 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.

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