Cambridge International AS & A Level
* 3 6 7 0 1 6 7 5 6 7 *
FURTHER MATHEMATICS 9231/42
Paper 4 Further Probability & Statistics May/June 2023
1 hour 30 minutes
You must answer on the question paper.
You will need: List of formulae (MF19)
INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● If additional space is needed, you should use the lined page at the end of this booklet; the question
number or numbers must be clearly shown.
● You should use a calculator where appropriate.
● You must show all necessary working clearly; no marks will be given for unsupported answers from a
calculator.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
INFORMATION
● The total mark for this paper is 50.
● The number of marks for each question or part question is shown in brackets [ ].
1 The lengths of the leaves of a particular type of tree are normally distributed with mean μ cm. The
lengths, x cm, of a random sample of 12 leaves of this type are recorded. The results are summarised as
follows.
2 The children at two large schools, P and Q, are all given the same puzzle to solve. A random sample
of size 10 is taken from the children at school P. Their individual times to complete the puzzle give a
sample mean of 9.12 minutes and an unbiased variance estimate of 2.16 minutes2. A random sample of
size 12 is taken from the children at school Q. Their individual times, x minutes, to complete the puzzle
are summarised by
/ x = 99.6 / (x - x ) 2 = 21.5,
where x is the sample mean. Times to complete the puzzle are assumed to be normally distributed with
the same population variance.
Test at the 5% significance level whether the population mean time taken to complete the puzzle by
children at school P is greater than the population mean time taken to complete the puzzle by children
at school Q. [8]
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller StudyTimeOT. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for £7.86. You're not tied to anything after your purchase.
