Work through the list without notes. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions.
Understanding
- I can explain what a continuous random variable is, and why only intervals (not single values) have probabilities. (Guide: “Continuous random variables”; Practice Q7)
- I can describe a normal curve as continuous, unimodal, symmetric and bell-shaped, fixed by μ and σ. (Guide: “The normal curve”)
- I can explain how a smaller or larger standard deviation changes the height and spread of a normal curve. (Guide: “How σ changes the curve”; Practice Q1)
- I can state the mean and standard deviation of the standard normal distribution and explain how z-scores link any normal distribution to it. (Guide: “The standard normal distribution”)
Skills
- I can use the 68–95–99.7 rule to estimate percentages, including strips on one side of the mean. (Guide: Worked example 1; Practice Q2)
- I can find the probability that a normal variable lies in an interval, showing the distribution, parameters, boundaries and direction. (Guide: Worked example 2; Practice Q3, Q4)
- I can turn a probability into an expected count. (Guide: Worked example 2(c); Practice Q4(b))
- I can find boundary values for the lowest, highest, middle and most extreme p% of a normal distribution. (Guide: Worked example 3; Practice Q5, Q6(c))
Reasoning
- I can compare the relative positions of values from two different normal distributions using percentiles. (Guide: Worked example 4; Practice Q6(a))
- I can judge whether a normal model is sensible for a variable, using its shape and context. (Guide: “Common misconceptions”; Practice Q7)
- I can interpret every probability or boundary in context, with units. (All worked examples)
All ticked? Move on to Topic 2.12, Sampling Distributions and the Central Limit Theorem, or return to the course roadmap.