Mathematics HL - Nov 2007 - P3

Mathematics HL - Nov 2007 - P3 - 1 hour IB DIPLOMA...

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IB DIPLOMA PROGRAMME PROGRAMME DU DIPLÔME DU BI PROGRAMA DEL DIPLOMA DEL BI N07/5/MATHL/HP3/ENG/TZ0/XX+ MATHEMATICS HIGHER LEVEL PAPER 3 Friday 16 November 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 signifcant fgures. 8807-7203 13 pages 1 hour © IBO 2007 88077203
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N07/5/MATHL/HP3/ENG/TZ0/XX+ 8807-7203 – 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 fnd 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: 11] Juan plays a quiz game. The scores he achieves on the separate topics may be modelled by independent normal distributions. (a) On the topic of sport, the scores have the distribution N( , ) 75 12 2 . Find the probability that Juan scores less than 57 points on the topic of sport. [2 marks] (b) On the topic of literature, Juan’s scores have a mean of 45, and 30 % of his scores are greater than 50. Find the standard deviation of his scores on the topic of literature. [3 marks] (c) Juan claims that he scores better in current affairs than in sport. He achieves the following scores on current affairs in 10 separate quizzes. 91 84 75 92 88 71 83 90 85 78 Perform a hypothesis test at the 5 % signiFcance level to decide whether there is evidence to support his claim. [6 marks]
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N07/5/MATHL/HP3/ENG/TZ0/XX+ 8807-7203 – 3 – Turn over 2. [Maximum mark: 20] (a) A horse breeder records the number of births for each of 100 horses during the past eight years. The results are summarized in the following table: Number of births 0 1 2 3 4 5 6 Frequency 1 5 26 37 18 12 1 Stating null and alternative hypotheses carry out an appropriate test at the 5 % signifcance level to decide whether the results can be modelled by B( , . ) 6 0 5 . [10 marks] (b) Without doing any Further calculations, explain brie±y how you would carry out a test, at the 5 % signifcance level, to decide iF the data can be modelled by B( , ) 6 p , where p is unspecifed. [2 marks] (c) A different horse breeder collected data on the time and outcome of births. The data are summarized in the following table:
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This note was uploaded on 04/24/2010 for the course MATH 137 taught by Professor Speziale during the Spring '08 term at Waterloo.

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Mathematics HL - Nov 2007 - P3 - 1 hour IB DIPLOMA...

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