AQA A-LEVEL FURTHER MATHEMATICS Paper 3 7367/3S STATISTICS|QUESTIONS & MARKING SCHEME MERGED| GRADED A+

A-level FURTHER MATHEMATICS Paper 3 Statistics Time allowed: 2 hours Materials l You must have the AQA Formulae and statistical tables booklet for A‑level Mathematics and A‑level Further Mathematics. l You should have a graphical or scientific calculator that meets the requirements of the specification. l You must ensure you have the other optional Question Paper/Answer Book for which you are entered (either Discrete or Mechanics). You will have 2 hours to complete both papers. Instructions l Use black ink or black ball‑point pen. Pencil should only be used for drawing. l Fill in the boxes at the top of this page. l Answer all questions. l You must answer each question in the space provided for that question. If you require extra space for your answer(s), use the lined pages at the end of this book. Write the question number against your answer(s). l Do not write outside the box around each page or on blank pages. l Show all necessary working; otherwise marks for method may be lost. l Do all rough work in this book. Cross through any work that you do not want to be marked. Information l The marks for questions are shown in brackets. l The maximum mark for this paper is 50. Advice l Unless stated otherwise, you may quote formulae, without proof, from the booklet. l You do not necessarily need to use all the space provided. Please write clearly in block capitals. Centre number Candidate number Surname ________________________________________________________________________ Forename(s) ________________________________________________________________________ Candidate signature ________________________________________________________________________ For Examiner’s Use Question Mark 1 2 3 4 5 6 7 8 TOTAL I declare this is my own work. DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED 2 There are no questions printed on this page Jun23/7367/3S Do not write outside the box (02) 3 Answer all questions in the spaces provided. 1 The discrete random variable A takes only the values 0, 2 and 4, and has cumulative distribution function F(a) ¼ P(A a) a 024 F(a) 0.2 0.6 1 Find P(A ¼ 2) Circle your answer. [1 mark] 0 0.4 0.6 0.8 2 The time, T days, between rain showers in a city in autumn can be modelled by an exponential distribution with mean 1.25 Find the distribution of the number of rain showers per day in the city. Tick (3) one box. [1 mark] Distribution Mean Exponential 0.8 Exponential 1.25 Poisson 0.8 Poisson 1.25 Do not write outside the box Jun23/7367/3S Turn over s (03) 4 3 The masses of tins of a particular brand of spaghetti are normally distributed with mean m grams and standard deviation 4.1 grams. A random sample of 11 tins of spaghetti has a mean mass of 401.8 grams. Construct a 98% confidence interval for m, giving your values to one decimal place. [3 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Do not write outside the box Jun23/7367/3S (04) 5 4 The random variable X has a normal distribution with unknown mean m and unknown variance s2 A random sample of 8 observations of X has mean x ¼ 101:5 and gives the unbiased estimate of the variance as s2 ¼ 4:8 The random sample is used to conduct a hypothesis test at the 10% level of significance with the hypotheses H0 : m ¼ 100 H1 : m 6¼ 100 Carry out the hypothesis test