AQA AS FURTHER MATHEMATICS RATING Paper 2 Statistics MAY 2023

AQA AS FURTHER MATHEMATICS Paper 2 Statistics Friday 19 May 2023 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. G/LM/Jun23/E5 7366/2S There are no questions printed on this page DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED box Answer all questions in the spaces provided. 1 The continuous random variable X has variance 9 The discrete random variable Y has standard deviation 2 and is independent of X Find Var(X + Y ) box Circle your answer. [1 mark] 5 11 13 85 2 The random variable T has a discrete uniform distribution and takes the values 1, 2, 3, 4 and 5 Find the variance of T Circle your answer. 1 4 5 3 2 13 6 [1 mark] Turn over for the next question Turn over U 3 The discrete random variable X has probability distribution box x – 4 3 8 P(X = x) 0.2 0.7 0.1 Show that E(5X – 7) = 3.5 [3 marks] 4 The proportion, p, of people in a particular town who use the local supermarket is unknown. A random sample of 30 people in the town is taken and each person is asked if they use the local supermarket. The manager of the supermarket claims that 35% of the people in the town use the local supermarket. The random sample is used to conduct a hypothesis test at the 5% level of significance with the hypotheses box H0: p = 0.35 H1: p  0.35 Show that the probability that a Type I error is made is 0.0356, correct to four decimal places. [4 marks] Turn over U 5 Rebekah is investigating the distances, X light years, between the Earth and visible stars in the night sky. She determines the distance between the Earth and a star for a random sample of 100 visible stars. The summarised results are as follows:  x = 35 522 and  x 2 = 5 (a) Calculate a 97% confidence interval for the population mean of X, giving your values to the nearest light year. box [5 marks] 5 (b) Mike claims that the population mean is 267 light years. Rebekah says that the confidence interval supports Mike’s claim. State, with a reason, whether Rebekah is correct. [1 mark] box Turn over for the next question Turn over U (07) 6 An insurance company models the number of motor claims received in 1 day using a Poisson distribution with mean 65 6 (a) Find the probability that the company receives at most 60 motor claims in 1 day. box Give your answer to three decimal places. [1 mark] 6 (b) The company receives motor claims using a telephone line which is open 24 hours a day. Find the probability that the company receives exactly 2 motor claims in 1 hour. Give your answer to three decimal places. [2 marks] 6 (c) The company models the number of property claims received in 1 day using a Poisson distribution with mean 23 Assume that the number of property claims received is independent of the number of motor claims received. 6 (c) (i) Find the standard deviation of the variable that represents the total number of motor claims and property claims received in 1 day. box Give your answer to three significant figures. [2 marks] 6 (c) (ii) Find the probability that the company receives a total of more than 90 motor claims and property claims in 1 day. Give your answer to three significant figures. [2 marks] Turn over for the next question Turn over U 7 A theatre has morning, afternoon and evening shows. On one particular day, the theatre asks all of its customers to state whether they enjoyed or did not enjoy the show. The results are summarised in the table. box Morning show Afternoon show Evening show Total Enjoyed 62 91 172 325 Not enjoyed 25 35 115 175 Total 87 126 287 500 The theatre claims that there is no association between the show that a customer attends and whether they enjoyed the show. 7 (a) Investigate the theatre’s claim, using a 2.5% level of significance. [8 marks]