5.5 The normal distribution

Understand the use of a normal distribution to model a continuous random variable, and use normal distribution tables.

Sketches of normal curves to illustrate distributions or probabilities may be required.

Taught in: The normal distribution — modelling continuous data, Standardising — from any normal curve to the table · 7 questions

Solve problems concerning a variable X, where X ~ N(μ, σ²), including finding the value of P(X > x₁), or a related probability, given the values of x₁, μ and σ, and finding a relationship between x₁, μ and σ given the value of P(X > x₁) or a related probability.

For calculations involving standardisation, e.g. Z = (X − μ)/σ, full details of the working should be shown.

Taught in: Working backwards — finding x, μ or σ from a probability, Standardising — from any normal curve to the table · 11 questions

Recall the conditions under which the normal distribution can be used as an approximation to the binomial distribution, and use this approximation, with a continuity correction, in solving problems.

n must be large enough that both np > 5 and nq > 5.

Taught in: The normal approximation to the binomial · 7 questions