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
$X \sim N(50, 16)$ . Find $P(X < 54)$ , to 4 d.p.
Level 2 · 2 marksTry it
2
$X \sim N(50, 16)$ . Find $P(X > 56)$ , to 4 d.p.
Level 2 · 2 marksTry it
3
$X \sim N(30, 25)$ .

Find $P(X < 38)$ , giving your answer to 4 decimal places. (2 marks)
Level 2 · 2 marksTry it
4
$X \sim N(30, 25)$ .

Find $P(X > 26)$ , giving your answer to 4 decimal places. (3 marks)
Level 2 · 3 marksTry it
5
A machine cuts wooden dowels.

The length of a dowel cut by the machine may be modelled by a normal distribution with mean $40.3$ millimetres and standard deviation $0.25$ millimetres.
(a) Find the probability that a randomly chosen dowel is $40$ millimetres long.

(1 mark)
(b) Find the probability that the length of a randomly chosen dowel is between $39.8$ millimetres and $40.6$ millimetres.

(1 mark)
(c) A carpenter takes two of these dowels at random.

Find the probability that both dowels have lengths between $39.8$ millimetres and $40.6$ millimetres.

(1 mark)
Level 2 · 3 marksTry it

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