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GCE JUN 2009 : AS, S1: Statistics1

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1 2 3 4 5 6 ADVANCED SUBSIDIARY (AS) General Certificate of Education 2009 7 8 9 Mathematics 10 Assessment Unit S1 12 assessing 13 Module S1: Statistics 1 14 AMS11 11 [AMS11] 15 MONDAY 1 JUNE, MORNING 16 17 18 19 20 21 TIME 1 hour 30 minutes. INSTRUCTIONS TO CANDIDATES 22 Write your Centre Number and Candidate Number on the Answer Booklet provided. 23 Answer all seven questions. Show clearly the full development of your answers. 24 Answers should be given to three significant figures unless otherwise stated. 25 You are permitted to use a graphic or scientific calculator in this paper. 26 27 INFORMATION FOR CANDIDATES The total mark for this paper is 75 Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each 29 question or part question. A copy of the Mathematical Formulae and Tables booklet is provided. 30 Throughout the paper the logarithmic notation used is ln z where it is noted that 31 ln z logez 28 32 33 34 35 4214 Answer all seven questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 Peter is working on his biology coursework. The data for the heights of his sample of plant shoots are given in Table 1 below. Table 1 Height (cm) 0 10 20 30 40 50 Frequency 6 17 34 13 5 Calculate the mean and standard deviation of Peter s data. 2 [5] In a certain town 14% of the population is left-handed. Eight customers in a supermarket are chosen at random and asked if they are left-handed. (i) Give two reasons why the binomial distribution would be suited to model this situation. [2] Find the probability: (ii) that exactly one customer is left-handed; (iii) that at least three customers are left-handed. 4214 [2] [4] 2 [Turn over 3 The probability distribution of the random variable X is shown in Table 2 below. Table 2 x 5 6 7 8 9 10 11 12 P(X = x) k k k k k k k k (i) Find k [2] (ii) Explain why E(X) = 8.5 [1] (iii) Find Var(X) [4] The random variable Y is related to X by Y = 2X 5 (iv) Find E(Y) and Var(Y) 4 [3] Footballer Paul is paid bonuses depending on the number of goals he scores. Last season Paul scored 21 goals in 35 games. Using a Poisson distribution, find the probability that: (i) he scores during a match; [4] (ii) he scores either one or two goals during a match. [3] Paul is paid a 1000 bonus if he scores either one or two goals during a match and a 5000 bonus if he scores three or more goals during a match. (iii) Find Paul s expected bonus per match. 4214 [5] 3 [Turn over 5 The masses of year 14 students at a large school are Normally distributed with mean kg and standard deviation 12 kg. Five per cent of students weigh more than 111.74 kg. (i) Show that = 92 [4] Find the probability that a student chosen at random: (ii) weighs less than 89 kg; [4] (iii) weighs between 89 kg and 98 kg. [4] Eighty per cent of students weigh less than W kg. (iv) Find W 4214 [4] 4 [Turn over 6 A continuous random variable, X, has the probability density function f(x) defined by kx f(x) = 2 2kx 0 0 x 2 2<x 3 otherwise Fig. 1 below shows the graph of the function f(x) f(x) 1 0 1 2 3 4 x Fig. 1 (i) Write down f(2) in terms of k 1 (ii) Hence or otherwise show that k = 3 [3] (iii) Using Fig. 1, or otherwise, find P(1 X 3) [3] (iv) Using Fig. 1, or otherwise, find the median of X 4214 [1] [5] 5 [Turn over 7 In a large school 8.2% of students study both Chemistry and French. One fifth of French students study Chemistry and one quarter of Chemistry students study French. Find the probability that a student chosen at random: (i) studies French; [2] (ii) studies Chemistry; [2] (iii) studies neither French nor Chemistry. [3] A student does not study Chemistry. (iv) Find the probability that the student studies French. [5] THIS IS THE END OF THE QUESTION PAPER 4214 6 [Turn over S 1/08 937-013-1

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Additional Info : Gce Mathematics June 2009 Assessment Unit S1 Module S1: Statistics1
Tags : General Certificate of Education, A Level and AS Level, uk, council for the curriculum examinations and assessment, gce exam papers, gce a level and as level exam papers , gce past questions and answer, gce past question papers, ccea gce past papers, gce ccea past papers

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