About this topic
Before you begin
Choose binomial and normal models, interpret their parameters and translate the event before calculating its probability.
Learning goals
- Choose and use a binomial probability model
- Calculate an event probability in a specified binomial model
- Calculate a conditional probability in a specified binomial model
- Calculate the expectation of a specified binomial count
- Calculate the variance of a specified binomial count
- Recover the unique binomial parameters from exact moments
- Find the least trial count satisfying a binomial probability threshold
- Represent random variables, expectations and variances
- Choose and use a normal probability model
- Calculate an event probability in a specified normal model
- Calculate a conditional probability in a specified normal model
- Recover a normal boundary from its specified tail probability
- Recover a normal mean from a probability and known variance
- Recover a normal variance from a probability and known mean
- Recover the unique normal mean and variance from two probabilities
- Calculate a linear combination's expectation from specified moments
- Calculate a linear combination's variance with justified dependence conditions
- Calculate a probability for a specified combination of normal variables
Syllabus statements covered
- Include: concept of discrete random variables; concept of binomial distribution B(n, p), its use as a probability model and conditions for suitability; mean and variance without proof. The concept of discrete random variables is for teaching and learning only.
- Include: concept of continuous random variables; concept of normal distribution as a continuous probability model with mean and variance; use of N(μ, σ²); standard normal distribution; finding P(X < x₁) or related probabilities given x₁, μ, σ, and finding a relationship between x₁, μ, σ given a probability; symmetry and properties of the normal curve; problems using E(aX + b) and Var(aX + b), and E(aX + bY) and Var(aX + bY) for independent X and Y. Exclude normal approximation to binomial distribution. The concept of continuous random variables is for teaching and learning only.
- Include: concept of discrete random variables; concept of binomial distribution B(n, p), its use as a probability model and conditions for suitability; mean and variance without proof. The concept of discrete random variables is for teaching and learning only.
- Include: concept of continuous random variables; concept of normal distribution as a continuous probability model with mean and variance; use of N(μ, σ²); standard normal distribution; finding P(X < x₁) or related probabilities given x₁, μ, σ, and finding a relationship between x₁, μ, σ given a probability; symmetry and properties of the normal curve; problems using E(aX + b) and Var(aX + b), and E(aX + bY) and Var(aX + bY) for independent X and Y. Exclude normal approximation to binomial distribution. The concept of continuous random variables is for teaching and learning only.
Choose a lesson
Work through them in order.
- Not startedBinomial models and calculator tailsNextChoose a binomial model, translate exact and conditional tails, recover parameters and combine component and box counts.
- Not startedNormal models and linear combinationsNextInterpret normal areas and inverse tails, recover parameters, and compare transformed or independent measurements under a model.