A-level · Statistical distributions

Finding normal probabilitiesExam-style questions

Finding P(X < a), P(X > a) and P(a < X < b) for a normal distribution as areas under the curve, and the inverse problem — finding the value x for a given probability (the inverse normal).

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35 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
In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.

The volume, $V$ ml, of coffee dispensed into a cup by a vending machine can be modelled by a normal distribution with mean 236 ml and standard deviation 6 ml.
(a) Find the probability that the machine dispenses 248 ml or more into a randomly chosen cup.

(2 marks)

The machine dispenses at least $d$ ml into 95% of cups.
(b) Find the value of $d$

(3 marks)
Level 3 · 5 marksTry it
2
$X \sim N(50, 16)$ . Find $P(46 < X < 56)$ , to 4 d.p.
Level 3 · 2 marksTry it
3
$X \sim N(20, 25)$ . Find $P(X < 28)$ , to 4 d.p.
Level 3 · 2 marksTry it
4
$X \sim N(100, 225)$ . Find the value $a$ such that $P(X < a) = 0.90$ , to 3 s.f.
Level 3 · 3 marksTry it
5
Scores are modelled by $X \sim N(500, 1600)$ . Find the score exceeded by the top $5\%$ of candidates, to 3 s.f.
Level 3 · 3 marksTry it

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