Edexcel A-Level Mathematics A2 S2.3.1 Continuous Uniform Questions

Practise modelling continuous uniform variables, deriving their density and calculating interval probabilities with verified Edexcel IAL questions.

Exam points

state the full pdf f(t)=1/(b-a) on a stated interval and 0 otherwise
calculate probabilities from interval lengths, including inequalities
use a uniform cutting or journey-time model to convert context into a probability interval

[Maximum number: 10]

The random variable W has a continuous uniform distribution over the interval [-6, a] where a is a constant.

Given that $\operatorname{Var}(W)=27$

(a)

Show that a=12.

[ 2 ]

(b)

Given that $\mathrm{P}(W>b)=\frac{3}{5}$

[ 4 ]

(i)

find the value of b

[ 2 ]

(ii)

Find $\mathrm{P}\left(-12<W<\frac{b}{2}\right)$ .

[ 2 ]

$\mathrm{P}\left(-12<W<\frac{b}{2}\right)=\mathrm{P}(-6<W<0.6)=\frac{0.6+6}{18}=\frac{11}{30}$

(c)

A piece of wood AB has length 160 cm. The wood is cut at random into 2 pieces.
Each of the pieces is then cut in half. The four pieces are used to form the sides of a rectangle.

Calculate the probability that the area of the rectangle is greater than $975 \mathrm{~cm}^{2}$

[ 4 ]

$\frac{5}{8}$

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Edexcel A-Level Mathematics A2 S2.3.1 Continuous Uniform Questions question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question (c)