A-level · Statistical distributions

Finding μ and σExam-style questions

Working backwards from given probabilities to find an unknown mean or standard deviation (or both) by standardising to a z-value and solving — including a pair of simultaneous equations when both are unknown.

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

DifficultyAll Level 3 Level 4 Level 5

1
$X \sim N(\mu, 16)$ and $P(X < 30) = 0.90$ . Find $\mu$ , to 3 s.f.
Level 3 · 3 marksTry it
2
$X \sim N(50, \sigma^2)$ and $P(X > 60) = 0.20$ . Find $\sigma$ , to 3 s.f.
Level 3 · 3 marksTry it
3
$X \sim N(\mu, \sigma^2)$ with $P(X < 20) = 0.10$ and $P(X < 40) = 0.75$ . Find $\mu$ and $\sigma$ , to 3 s.f.
Level 3 · 4 marksTry it
4
$X \sim N(\mu, \sigma^2)$ with $P(X > 50) = 0.30$ and $P(X > 20) = 0.80$ . Find $\mu$ and $\sigma$ , to 3 s.f.
Level 3 · 4 marksTry it
5
$X \sim N(100, \sigma^2)$ and $P(X < 115) = 0.95$ . Find $\sigma$ , to 3 s.f.
Level 3 · 3 marksTry it

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