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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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