A-level FURTHER MATHEMATICS Paper 3 Statistics

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 scientific calculator that meets the requirements of the specification. (You may use a graphical calculator.) 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 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. 2 Answer all questions in the spaces provided. 1 The discrete uniform distribution X can take values 1, 2, 3, …, 10 Find P(X 7) Circle your answer. [1 mark] 0.3 0.4 0.6 0.7 2 The random variable X has variance Var (X) Which of the following expressions is equal to Var (aX þ b), where a and b are non-zero constants? Circle your answer. [1 mark] aVar (X) aVar (X) þ b a2 Var (X) a2 Var (X) þ b Jun21/7367/3S Do not write outside the box (02) 3 3 In a game, it is only possible to score 10, 20 or 30 points. The probability of scoring 20 points is twice the probability of scoring 30 points. The probability of scoring 20 points is half the probability of scoring 10 points. 3 (a) Find the mean points scored when the game is played once, giving your answer to two decimal places. [3 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 3 (b) Mina plays the game. Her father, Michael, tells her that he will multiply her score by 5 and then subtract 10 He will then give her the value he has calculated in pence rounded to the nearest penny. Calculate the expected value in pence that Mina receives