A-Level Maths Specification

OCR A H240

Section 2.04: Statistical distributions

Are you studying this syllabus?

You can track your progress by adding it to your account.

Add syllabus

#2.04a

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.]

#2.04b

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

Binomial distribution

#2.04c

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

#2.04d

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

#2.04e

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

#2.04f

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

#2.04g

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

#2.04h

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