Understand and be able to use simple, finite, discrete probability distributions, defined in the form of a table or a formula such as:
$P(X=x) = 0.05x(x + 1)$ for $x = 1, 2, 3$.

[Calculation of mean and variance of discrete random variables is excluded.]

Understand and be able to use the binomial distribution as a model.

Binomial distribution

Be able to calculate probabilities using the binomial distribution, using appropriate calculator functions.

Includes understanding and being able to use the formula
$P(X=x) = \dbinom{n}{x}p^x(1-p)^{n-x}$ and the notation $X ∼ B(n,p)$.

Learners should understand the conditions for a random variable to have a binomial distribution, be able to identify which of the modelling conditions (assumptions) is/are relevant to a given scenario and be able to explain them in context. They should understand the distinction between conditions and assumptions.

Binomial distribution

Know and be able to use the formulae $\mu = np$ and $\sigma^2 = npq$ when choosing a particular normal model to use as an approximation to a binomial model.

Approximating the binomial distribution

Understand and be able to use the normal distribution as a model.

Includes understanding and being able to use the notation $X ∼ N(\mu, \sigma^2)$.

Normal distribution

Be able to find probabilities using the normal distribution, using appropriate calculator functions.

This includes finding $x$, for a given normal variable, when $P(X < x)$ is known.

Learners should understand the standard normal distribution, $Z$, and the transformation $Z = \dfrac{X-\mu}{\sigma}$.

Normal distribution

Understand links to histograms, mean and standard deviation.

Learners should know and be able to use the facts that in a normal distribution,
1. about two-thirds of values lie in the range $\mu \pm \sigma$,
2. about 95% of values lie in the range $\mu \pm 2\sigma$,
3. almost all values lie in the range $\mu \pm 3\sigma$ and
4. the points of inflection in a normal curve occur at $x = \mu \pm \sigma$.

[The equation of the normal curve is excluded.]

Normal distribution

Be able to select an appropriate probability distribution for a context, with appropriate reasoning, including recognising when the binomial or normal model may not be appropriate.

Includes understanding that a given binomial distribution with large n can be approximated by a normal distribution.

[Questions explicitly requiring calculations using the normal approximation to the binomial distribution are excluded.]

Use probability distributions in context