A-level · Statistical distributions

The normal distributionExam-style questions

The normal model N(μ, σ²) for continuous data — its symmetric bell shape, mean = median = mode = μ, spread set by σ, and standardising any normal variable to the standard normal Z = (X − μ)/σ.

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16 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
The mass $X$ kg of an item is modelled by $X \sim N(60, 64)$ . Write down the mean and the standard deviation of $X$ .
Level 2 · 2 marksTry it
2
$X \sim N(20, 25)$ . Approximately $95\%$ of values lie within two standard deviations of the mean. Between which two values is this?
Level 2 · 2 marksTry it
3
$X \sim N(60, 64)$ . Find the $z$ -score of the value $X = 72$ .
Level 3 · 2 marksTry it
4
$X \sim N(100, 225)$ . Find the $z$ -scores of $X = 85$ and $X = 130$ .
Level 3 · 2 marksTry it
5
$X \sim N(50, \sigma^2)$ and $P(X < 60) = 0.84$ . Find $P(X > 60)$ and $P(40 < X < 60)$ .
Level 3 · 3 marksTry it

11 more questions on the normal distribution

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