#Statistics #Year12 #Standard >[!info]- [The normal distribution | NSW Curriculum Website](https://curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-standard-11-12-2024/content/n12-tba2/fa92309f60) >- MST-12-S2-10 analyses normally distributed datasets using statistical processes ## 📖 Prior Knowledge | Content | Prior knowledge | Used for | | --------------------------------------------------- | ---------------------------------------- | ---------------------------------- | | [[Stage 6 Standard 2/Data Analysis\|Data Analysis]] | - summary statistics, shape of a dataset | - identifying normal distributions | | [[Data Analysis A]] | - standard deviation | - empirical rule | ## Normally distributed datasets - Recognise that a dataset that is normally distributed can be represented by a bell-shaped curve - Explain that the mean, median and mode are approximately equal for data arising from a random variable that is normally distributed ## Calculating z-scores - Describe the $z$-score as the number of standard deviations that a value is above or below the mean - Recognise that the set of $z$-scores for data arising from a random variable that is normally distributed has a mean of 0 and standard deviation of 1 - Calculate the $z$-score corresponding to a specific value in a dataset by applying the formula - $z=\frac{x\ -\ \mu}{\sigma}$, where $x$ is a specific value, $\mu$ is the mean and $\sigma$ is the standard deviation - Use $z$-scores to compare scores from different datasets and justify conclusions in the context of the problem ## Probability using z-scores - Calculate probabilities using $z$-scores and the empirical rule - Represent probabilities by shading areas under the normal distribution curve - Use $z$-scores to identify probabilities of events less or more extreme than a given event and solve problems - Use $z$-scores to make judgements related to outcomes of a given event or sets of data