Continuous probability and normal distributions.
Build continuous probability models using areas, then use normal distributions, independent sums and sample means to answer practical questions.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Probability density functions and total area
Recognise a valid density and find its normalising constant.
- 02
Interval probabilities by integration
Translate interval events into definite integrals.
- 03
Cumulative distribution functions
Build and use a cumulative distribution across its complete domain.
- 04
Mean, variance and standard deviation for continuous models
Calculate the mean, second moment and spread of a continuous model.
- 05
Normal distributions
Recognise the shape, parameters and limitations of normal models.
- 06
Standardisation and z-scores
Express normal measurements on a common standard-deviation scale.
- 07
Normal probabilities and inverse-normal values
Calculate normal interval probabilities and reverse them to find cut-offs.
- 08
Independent sums and sample means
Find distributions of independent normal sums and sample means.
- 09
Sampling variation and distributions of sample means
Explain sampling variation and when a normal approximation for a mean is justified.
Topic review
Revisit the key ideas, then choose a practice paper.