Pearson Edexcel IAL Mathematics S2.3 Continuous distributions Question Bank

Practise continuous uniform models and normal approximations, including density functions, interval probabilities and continuity corrections.

Exam points

state a uniform pdf over its interval and use interval length to calculate probabilities
choose a normal approximation and apply a continuity correction before standardising

Covered syllabus points

S2.3.1 - continuous uniform S2.3.2 - Normal approximation to the binomial distribution

[Maximum number: 4]

Navtej travels to work by train. A train leaves the station every 7 minutes and Navtej's arrival at the station is independent of when the train is due to leave.

(a)

Write down a suitable model for the distribution of the time, T minutes, that he has to wait for a train to leave.

[ 1 ]

(b)

Find the mean and standard deviation of T

During a 10-week period, Navtej travels to work by train on 46 occasions.

[ 3 ]

mean =3.5

B1

standard deviation $=\sqrt{\frac{(7-0)^{2}}{12}}$ $=\frac{7}{\sqrt{12}}=2.0207 \ldots$

awrt 2.02

A1

[Maximum number: 3]

In a peat bog, Common Spotted-orchids occur at a mean rate of 4.5 per $\mathrm{m}^{2}$

Assuming that in the peat bog, Common Spotted-orchids still occur at a mean rate of 4.5 per m^2

use a normal approximation to find the probability that in a randomly selected 20 m^2 of the peat bog there are fewer than 70 Common Spotted-orchids.

$T \sim \mathrm{~N}(90,90)$

B1

$\mathrm{P}(T<70)=\mathrm{P}\left(Z< \pm\left(\frac{69.5-90}{\sqrt{90}}\right)\right) \text { or } \mathrm{P}(Z< \pm 2.160 \ldots \ldots)$
=0.0154

awrt 0.0154

A1

(3)

All question bank results loaded

Covered syllabus points

S2.3 - Continuous distributions question 1

Question (a)

Question (b)

S2.3 - Continuous distributions question 2