Official June 2024 AQA AS FURTHER MATHEMATICS 7366/2S Paper 2 Statistics Merged Question Paper + Mark Scheme Ace your Mocks!!! G/LM/Jun24/G4001/V6 7366/2S (JUN2473662S01) AS FURTHER MATHEMATICS Paper 2 Statistics Friday 17 May 2024 Afternoon Time allowed: 1 hour 30 minutes Materials  You must have the AQA Formulae and statistical tables booklet for A-level Mathematics and A-level Further Mathematics.  You should have a graphical or scientific calculator that meets the requirements of the specification.  You must ensure you have the other optional Question Paper/Answer Book for which you are entered (either Discrete or Mechanics). You will have 1 hour 30 minutes to complete both papers. Instructions  Use black ink or black ball-point pen. Pencil should only be used for drawing.  Fill in the boxes at the top of this page.  Answer all questions.  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).  Do not write outside the box around each page or on blank pages.  Show all necessary working; otherwise marks for method may be lost.  Do all rough work in this book. Cross through any work that you do not want to be marked. Information  The marks for questions are shown in brackets.  The maximum mark for this paper is 40. Advice  Unless stated otherwise, you may quote formulae, without proof, from the booklet.  You do not necessarily need to use all the space provided. For Examiner’s Use Question Mark 1 2 3 4 5 6 7 TOTAL Please write clearly in block capitals. Centre number Candidate number Surname _________________________________________________________________________ Forename(s) _________________________________________________________________________ Candidate signature _________________________________________________________________________ I declare this is my own work. 2 Do not write outside the box (02) G/Jun24/7366/2S Answer all questions in the spaces provided. 1 The discrete random variable X has probability distribution function P(X = x) = 0.45 x = 1 0.25 x = 2 0.25 x = 3 0.05 x = 4 0 otherwise { State the mode of X Circle your answer. [1 mark] 0.25 0.45 1 2.5 2 A test for association is to be carried out. The tables below show the observed frequencies and the expected frequencies that are to be used for the test. Observed X Y Z Expected X Y Z A 28 6 66 A 45 15 40 B 884 B 938 C 54 16 10 C 36 12 32 It is necessary to merge some rows or columns before the test can be carried out. Find the entry in the tables that provides evidence for this. Circle your answer. [1 mark] Observed A-Z Observed B-Z Expected A-X Expected B-Y 3 Do not write outside the box (03) G/Jun24/7366/2S Turn over 8 3 The random variable X has a normal distribution with known variance 15.7 A random sample of size 120 is taken from X The sample mean is 68.2 Find a 94% confidence interval for the population mean of X Give your limits to three significant figures. [3 marks] ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ Turn over for the next question 4 Do not write outside the box (04) G/Jun24/7366/2S 4 The discrete random variable Y has probability distribution y 15 21 36 43 P(Y = y) 0.16 0.32 0.29 0.23 The standard deviation of Y is s 4 (a) Show that s = 10.53 correct to two decimal places. [4 marks] ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ 5 Do not write outside the box (05) G/Jun24/7366/2S Turn over 8 4 (b) The median of Y is m Find P(Y > m – 1.5 s) [3 marks] ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ Turn over for the next question 6 Do not write outside the box (06) G/Jun24/7366/2S 5 A spinner has 8 equal areas numbered 1 to 8, as shown in the diagram below. 8 4 2 7 1 5 3 6 The spinner is spun and lands with one of its edges on the ground. 5 (a) Assume that the spinner lands on each number with equal probability. 5 (a) (i) State a distribution that could be used to model the number that the spinner lands on. [1 mark] ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ 5 (a) (ii) Use your distribution from part 5 (a) (i) to find the probability that the spinner lands on a number greater than 5 [1 mark] ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ 7 Do not write outside the box (07) G/Jun24/7366/2S Turn over 8 5 (b) Clare spins the spinner 1000 times and records the results in the following table. Number landed on 12345678 Frequency 37 64 112 161 308 156 109 53 5 (b) (i) Explain how the data shows that the model used in part (a) may not be valid. [2 marks] ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ 5 (b) (ii) Describe how Clare’s results could be used to adjust the model. [2 marks] ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ 8 Do not write outside the box (08) G/Jun24/7366/2S 6 The continuous random variable X has probability density function f(x) = 3x 44 + 1 22 1 ≤ x ≤ 5 0 otherwise { 6 (a) Find P(X > 2) [2 marks] ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ 6 (b) Find the upper quartile of X Give your answer to two decimal places. [4 marks] ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ 9 Do not write outside the box (09) G/Jun24/7366/2S Turn over 8 6 (c) Find Var(44X –3) Give your answer to three decimal places. [5 marks] ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ 10 Do not write outside the box G/Jun24/7366/2S (10) 7 Over a period of time, it has been shown that the mean number of customers entering a small store is 6 per hour. The store runs a promotion, selling many products at lower prices. 7 (a) Luke randomly selects an hour during the promotion and counts 11 customers entering the store. He claims that the promotion has changed the mean number of customers per hour entering the store. Investigate Luke’s claim, using the 5% level of significance. [6 marks]