> Thursday 7 October 2021 – Afternoon A Level Further Mathematics B (MEI) Y432/01 Statistics Minor

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Answer all the questions. 1 The probability distribution of a discrete random variable X is given by the formula P( ) X r = = k r ^( ) - + 1 1 2 h for r = 1, 2, 3, 4, 5. (a) Show that k = 35 1 . [2... ] The distribution of X is shown in the table. r 1 2 3 4 5 P( ) X r = 35 1 35 2 7 1 7 2 35 17 (b) Comment briefly on the shape of the distribution. [1] (c) Find each of the following. • E(X  ) • Var(X  ) [2] The random variable Y is given by Y X = - 5 10. (d) Find each of the following. • E(Y  ) • Var(Y  ) [2]3 © OCR 2021 Y432/01 Oct21 Turn over 2 A road transport researcher is investigating the link between the age of a person, a years, and the distance, d metres, at which the person can read a large road sign. The researcher selects 13 individuals of different ages between 20 and 80 and measures the value of d for each of them. The spreadsheet below shows the data which the researcher obtained, together with a scatter diagram which illustrates the data. A 123456789 10 11 12 13 14 15 16 B C D E F G H I J Age (years) 20 25 30 35 40 45 50 55 60 65 70 75 80 Distance (metres) 170 185 155 170 150 135 125 140 140 150 110 95 120 Distance Age 0 80 100 120 140 160 180 200 20 40 60 80 100 (a) Explain which of the two variables a and d is the independent variable. [1] (b) Find the equation of the regression line of d on a. [2] (c) Use the regression line to predict the average distance at which a 60-year-old person can read the road sign. [1] (d) Explain why it might not be sensible to use the regression line to predict the average distance at which a 5-year-old child can read the road sign. [2] (e) Determine the value of the residual for a = 40. [2 [Show More]

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