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GCE JUN 2006 : AS, S1: Statistics1

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ADVANCED SUBSIDIARY (AS) General Certificate of Education 2006 Mathematics assessing Module S1: Statistics 1 AMS11 Assessment Unit S1 [AMS11] TUESDAY 6 JUNE, AFTERNOON TIME 1 hour 30 minutes. INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number on the Answer Booklet provided. Answer all seven questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. You are permitted to use a graphic or scientific calculator in this paper. 1 8.6.05RTS 2 24.10.05ES 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 question or part question. A copy of the Mathematical Formulae and Tables booklet is provided. Throughout the paper the logarithmic notation used is ln z where it is noted that ln z log e z AMS1S6 849 Answer all seven questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 The probability distribution of the random variable X is shown in Table 1 below. Table 1 x 1 2 3 4 5 6 7 8 P(X = x) 0.1 0.11 0.125 0.14 0.16 0.13 0.115 0.12 (i) Find P(2 X < 6). [2] (ii) Find E(X ) and Var(X ). 2 [6] Flaws in the production of electric cable are known to occur at an average rate of two per kilometre. [3] (ii) A three-kilometre length is tested. Find the probability that at least one flaw is found. [4] 1 8.6.05RTS 2 24.10.05ES (i) A one-kilometre length is tested. Find the probability that exactly two flaws are found. AMS1S6 849 2 [Turn over 3 An editor wishes to assess the occurrence of typing errors in her newspaper. She carries out an analysis of a large sample of pages from recent issues. A summary of the findings is given in Table 2 below. Table 2 Number of errors 0 1 2 3 4 5 6 Number of pages 268 403 297 153 59 14 6 (i) Find the mean and variance of the number of errors per page. (ii) Which probability distribution could be used to model the number of typing errors per page in the newspaper? 4 [4] [1] A forester plants ten sapling birch trees. The success rate for saplings developing to maturity is 85%. Find the probability that: (i) exactly eight saplings develop to maturity, [3] (ii) at least eight saplings develop to maturity, [4] (iii) at most eight saplings develop to maturity. [2] In a second area of the forest, the forester has already planted a number of sapling birch trees. His expected number of trees developing to maturity in this area is 13.6 (iv) (a) Find how many trees were planted in the second area of the forest. [3] 1 8.6.05RTS 2 24.10.05ES (b) Find the probability that exactly one of these saplings does not develop to maturity. [2] AMS1S6 849 3 [Turn over 5 The continuous random variable X has probability density function f(x) where kx 2 f ( x) = 0 2 < x < 44 x otherwise where k is a constant. (i) Show that k = 3 56 (ii) Find E(X ) and Var(X ). [8] (iii) Find P(X 6 [4] [3] 3). Following a survey of leisure interests of students at a large university it was found that 48% of rugby players were swimmers, and 25% of swimmers were rugby players. Suppose the events R and S are: R: a student chosen at random is a rugby player, S: a student chosen at random is a swimmer. Also suppose that p is the probability that a student chosen at random is both a rugby player and a swimmer. (i) Show that P( R) = p 0.48 [3] (ii) Find P(S) in terms of p. [1] Sixty-one percent of students were swimmers or rugby players or both. [5] (iv) Are the events R and S independent? Justify your answer. [2] 1 8.6.05RTS 2 24.10.05ES (iii) Find P(R) and P(S). AMS1S6 849 4 [Turn over 7 The masses of a particular variety of onion are Normally distributed with mean 170 grams and standard deviation 25 grams. The onions are packaged according to mass into three grades. Grade A onions weigh 185 grams or more. (i) Find, to 4 decimal places, the probability that an onion chosen at random is a Grade A onion. [5] Grade B onions weigh between 140 grams and 185 grams. (ii) Find, to 4 decimal places, the probability that an onion chosen at random is a Grade B onion. [5] The remainder of onions are Grade C. The cost of production of the onions is 32 pence per kilogram. Grade A onions are sold at 50 pence per kilogram, Grade B onions are sold at 42 pence per kilogram and Grade C onions are sold at 30 pence per kilogram. (iii) Find the expected profit per kilogram of onions sold. Give your answer to the nearest 0.1 pence per kilogram. [5] 1 8.6.05RTS 2 24.10.05ES THIS IS THE END OF THE QUESTION PAPER AMS1S6 849 5 [Turn over 1 8.6.05RTS 2 24.10.05ES 1 8.6.05RTS 2 24.10.05ES 2 24.10.05ES 1 8.6.05RTS S 6/05 4300 302507(50) [Turn over

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Additional Info : Gce Mathematics June 2006 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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