OCR 2023 GCE FURTHER MATHEMATICS B MEI Y422/01: STATISTICS MAJOR A LEVEL QUESTION PAPER & MARK SCHEME (MERGED)

FURTHER MATHEMATICS B MEI STATISTICS MAJOR OCR 2023 GCE FURTHER MATHEMATICS B MEI Y422/01: STATISTICS MAJOR A LEVEL QUESTION PAPER & MARK SCHEME (MERGED) You must have: • the Printed Answer Booklet • the Formulae Booklet for Further Mathematics B (MEI) • a scientific or graphical calculator QP Oxford Cambridge and RSA Friday 16 June 2023 – Afternoon A Level Further Mathematics B (MEI) Y422/01 Statistics Major Time allowed: 2 hours 15 minutes INSTRUCTIONS • Use black ink. You can use an HB pencil, but only for graphs and diagrams. • Write your answer to each question in the space provided in the Printed Answer Booklet . If you need extra space use the lined pages at the end of the Printed Answer Booklet. The question numbers must be clearly shown. • Fill in the boxes on the front of the Printed Answer Booklet. • Answer all the questions. • Where appropriate, your answer should be supported with working. Marks might be given for using a correct method, even if your answer is wrong. • Give your final answers to a degree of accuracy that is appropriate to the context. • Do not send this Question Paper for marking. Keep it in the centre or recycle it. INFORMATION • The total mark for this paper is 120. • The marks for each question are shown in brackets [ ]. • This document has 12 pages. ADVICE • Read each question carefully before you start your answer. 2 © OCR 2023 Y422/01 Jun23 1296 Section A (25 marks) 1 A website simulates the outcome of throwing four fair dice. Ten thousand people take part in a challenge using the website in which they have one attempt at getting four sixes in the four throws of the dice. The number of people who succeed in getting four sixes is denoted by the random variable X. (a) Show that, for each person, the probability that the person gets four sixes is equal to 1 . [1] (b) Explain why you could use either a binomial distribution or a Poisson distribution to model the distribution of X. [3] (c) Use a Poisson distribution to calculate each of the following probabilities. • P(X = 10) • P(X 2 10) [3] (d) In another challenge on the website, 50 people are each given 20 independent attempts to try to get four sixes as often as they can. Determine the probability that no more than 2 people succeed in getting four sixes at least once in their 20 attempts. [3] 3 Turn over © OCR 2023 Y422/01 Jun23 2 A student is investigating the link between temperature and electricity consumption in the winter months. The student finds the average minimum temperature, x °C, from across the country on a day. The student then finds the total electricity consumption for that day, y GWh. The scatter diagram below shows the values of x and y obtained from a random sample of 10 winter days. It also shows the equation of the regression line of y on x and the value of r2, where r is the product moment correlation coefficient. y -4 -2 0 x 2 4 6 8 10 (a) Use the regression line to estimate the electricity consumption at each of the following average minimum temperatures. • 5 °C • -4 °C [2] (b) Comment on the reliability of your estimates. [3] 1150 1100 1050 y =-10.26 x + 1013 r2 = 0.5986 1000 950 900