Mathematics — previous courses · 2009 · May · Paper 2 · HL · TZ1 · Question paper

M09/5/MATHL/HP2/ENG/TZ1/XX mathematics h igher level Pa Per 2 Friday 8 May 2009 (morning) iNs Truc Tio Ns To c ANdid ATEs  Write your session number in the boxes above.  d o not open this examination paper until instructed to do so.  A graphic display calculator is required for this paper.  section A: answer all of section A in the spaces provided.  section B: answer all of section B on the answer sheets provided. Write your session number on each answer sheet, and attach them to this examination paper and your cover sheet using the tag provided.  At the end of the examination, indicate the number of sheets used in the appropriate box on your cover sheet.  unless otherwise stated in the question, all numerical answers must be given exactly or correct to three significant figures. 2209-7204 13 pages 2 hours c andidate session number 0 0 © international Baccalaureate organization 2009 0113 22097204 M09/5/MATHL/HP2/ENG/TZ1/XX 2209-7204 – 2 – 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 Answer all the questions in the spaces provided. Working may be continued below the lines, if necessary. 1. [Maximum mark: 6] Bob measured the heights of 63 students. After analysis, he conjectured that the height, H , of the students could be modelled by a normal distribution with mean 166.5 cm and standard deviation 5 cm. (a) Based on this assumption, estimate the number of these students whose height is at least 170 cm. [3 marks] Later Bob noticed that the tape he had used to measure the heights was faulty as it started at the 5 cm mark and not at the zero mark. (b) What are the correct values of the mean and variance of the distribution of the heights of these students? [3 marks] . . . . . . . . . . .