Prime DSE Series - Mathematics Mock Exam Papers (Extended Part) Module 1 Set 3

HKDSE-MATH-EP(M1)(Set 3) − 12 12 © United Prime Educational Publishing (HK) Ltd. Answers written in the margins will not be marked. Answers written in the margins will not be marked. Answers written in the margins will not be marked. SECTION B (50 marks) 9. The scores obtained by a group of students in an exam follows a normal distribution with a mean of µ and a standard deviation of 8. (a) A sample of 10 students are randomly selected and their scores are recorded below: 64, 72, 60, 74, 78, 66, 76, 90, 92, 80 (i) Construct a 95% confidence interval for µ . (ii) Find the least sample size to be taken such that the width of a 97% confidence interval for µ is less than 5. (7 marks) (b) Suppose that µ = 76. A student who scores higher than 88 will be certificated. The students in the group are randomly selected one by one and their scores are recorded. The recording stops when 2 certificated students are found. (i) Find the probability that the scores of more than 9 students are recorded. (ii) Given that the scores of more than 9 students are recorded, find the probability that the scores of exactly 11 students are recorded. (5 marks) Sample © United Prime Educational Publishing (HK) Limited All rights reserved; no part of this publication may be reproduced, photocopied, recorded or otherwise, without the prior written permission of the Publisher.