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Mathematics HL - May 2007 TZ2 - P3

Mathematics HL - May 2007 TZ2 - P3 - 1 hour IB DIPLOMA...

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IB DIPLOMA PROGRAMME PROGRAMME DU DIPLÔME DU BI PROGRAMA DEL DIPLOMA DEL BI M07/5/MATHL/HP3/ENG/TZ2/XX+ MATHEMATICS HIGHER LEVEL PAPER 3 Wednesday 16 May 2007 (afternoon) INSTRUCTIONS TO CANDIDATES Do not open this examination paper until instructed to do so. Answer all the questions in one section only. Unless otherwise stated in the question, all numerical answers must be given exactly or correct to three significant figures. 2207-7209 9 pages 1 hour © IBO 2007 22077209
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M07/5/MATHL/HP3/ENG/TZ2/XX+ 2207-7209 – 2 – Please start each question on a new page. Full marks are not necessarily awarded for a correct answer with no working. Answers must be supported by working and/or explanations. In particular, solutions found from a graphic display calculator should be supported by suitable working, e.g. if graphs are used to find a solution, you should sketch these as part of your answer. Where an answer is incorrect, some marks may be given for a correct method, provided this is shown by written working. You are therefore advised to show all working. SECTION A Statistics and probability 1. [Maximum mark: 8] (a) The random variable X has a geometric distribution with parameter p = 1 4 . What is the value of P( X 4) ? [3 marks] (b) A magazine publisher promotes his magazine by putting a concert ticket at random in one out of every four magazines. If you need 8 tickets to take friends to the concert, what is the probability that you will find your last ticket when you buy the 20th magazine? [3 marks] (c) How are the two distributions in parts (a) and (b) related? [2 marks] 2. [Maximum mark: 14] (a) In a random sample of 1100 people in Switzerland it was found that 580 of them had a connection to the Internet. Calculate the 95 % confidence interval for the proportion of people in Switzerland having a connection to the Internet. [7 marks] (b) How large should the sample have been to make the width of the 95 % confidence interval less than 0.02 ? [7 marks]
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M07/5/MATHL/HP3/ENG/TZ2/XX+ 2207-7209 – 3 – Turn over 3. [Maximum mark: 14]
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