PMT ForExaminer’sUse CentreNumber CandidateNumber Surname OtherNames Examiner’sInitials CandidateSignature Question Mark General Certificate of Education 1 Advanced Subsidiary Examination June 2014 2 3 Statistics SS1B 4 Unit Statistics 1B 5 6 Thursday 22 May 2014 9.00 am to 10.30 am 7 For this paper you must have: TOTAL * the blue AQA booklet offormulae and statistical tables. You mayuse a graphics calculator. Time allowed * 1 hour 30 minutes 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. * Write the question part reference (eg (a), (b)(i) etc) in the left-hand margin. * You must answer each question in the space provided for that question. If you require extra space, use an AQA supplementary answer book; do not use the space provided for a different question. * Do not write outside the box around each page. * 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. * The final answer to questions requiring the use of tables or calculators should normally be given to three significant figures. Information * The marks for questions are shown in brackets. * The maximum mark for this paper is 75. * Unit Statistics 1B has a written paper only. Advice * Unless stated otherwise, you may quote formulae, without proof, from the booklet. * You do not necessarily need to use all the space provided. (JUN14SS1B01) SS1B P81378/Jun14/E2 PMT Donotwrite 2 outsidethe box Answer all questions. Answer each question in the space provided for that question. 1 The weights, in kilograms, of a random sample of 15 items of cabin luggage on an aeroplane were as follows. 4.6 3.8 3.9 4.5 4.9 3.6 3.7 5.2 4.0 5.1 4.1 3.3 4.7 5.0 4.8 For these data: (a) find values for the median and the interquartile range; [4 marks] (b) find the value for the range; [1 mark] (c) state why the mode is not an appropriate measure of average. [1 mark] QUESTION Answer space for question 1 PART REFERENCE ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. (02) P/Jun14/SS1B PMT Donotwrite 3 outsidethe box QUESTION Answer space for question 1 PART REFERENCE ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. Turn over s (03) P/Jun14/SS1B PMT Donotwrite 4 outsidethe box 2 (a) Tim rings the church bell in his village every Sunday morning. The time that he spends ringing the bell may be modelled by a normal distribution with mean 7.5 minutes and standard deviation 1.6 minutes. Determine the probability that, on a particular Sunday morning, the time that Tim spends ringing the bell is: (i) at most 10 minutes; (ii) more than 6 minutes; (iii) between 5 minutes and 10 minutes. [6 marks] (b) June rings the same church bell for weekday weddings. The time that she spends, in minutes, ringing the bell may be modelled by the distribution Nðm, 2:42Þ. Given that 80 per cent of the times that she spends ringing the bell are less than 15 minutes, find the value of m. [4 marks] QUESTION Answer space for question 2 PART REFERENCE ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. (04) P/Jun14/SS1B PMT Donotwrite 5 outsidethe box QUESTION Answer space for question 2 PART REFERENCE ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. Turn over s (05) P/Jun14/SS1B PMT Donotwrite 6 outsidethe box QUESTION Answer space for question 2 PART REFERENCE ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. (06) P/Jun14/SS1B PMT Donotwrite 7 outsidethe box QUESTION Answer space for question 2 PART REFERENCE ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. Turn over s (07) P/Jun14/SS1B PMT Donotwrite 8 outsidethe box 3 The table shows the body mass index (BMI), x, and the systolic blood pressure (SBP), y mmHg, for each of a random sample of 10 men, aged between 35 years and 40 years, from a particular population. x 13 23 29 35 17 34 25 20 31 27 y 103 115 124 126 108 120 113 117 118 119 (a) Calculate the equation of the least squares regression line of y on x. [4 marks] (b) Use your equation to estimate the SBP of a man from this population who is aged 38 years and who has a BMI of 30. [2 marks] (c) State why your equation might not be appropriate for estimating the SBP of a man from this population: (i) who is aged 38 years and who has a BMI of 45; (ii) who is aged 50 years and who has a BMI of 25. [2 marks] (d) Find the value of the residual for the point ð20, 117Þ. [2 marks] (e) The mean of the vertical distances of the 10 points from the regression line calculated in part (a) is 2.71, correct to three significant figures. Comment on the likely accuracy of your estimate in part (b). 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(08) P/Jun14/SS1B PMT Donotwrite 9 outsidethe box QUESTION Answer space for question 3 PART REFERENCE ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. Turn over s (09) P/Jun14/SS1B PMT Donotwrite 10 outsidethe box QUESTION Answer space for question 3 PART REFERENCE ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. (10) P/Jun14/SS1B