# Distributed with a mean of 1875 cm and a standard

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Unformatted text preview: es. A machine produces cloth with some minor faults. The number of faults per metre is a random variable following a Poisson distribution with a mean 3. Calculate the probability that a metre of the cloth contains five or more faults. (Total 4 marks) 499. Give your answers to four significant figures. The following is a random sample of 16 measurements of the density of aluminium. Assume that the measurements are normally distributed. 2.704 2.709 2.711 2.706 2.708 2.705 2.709 2.701 2.705 2.707 2.710 2.700 2.703 2.699 2.702 2.701 Construct a 95 % confidence interval for the density of aluminium, showing all steps clearly. (Total 6 marks) 500. Give your answers to four significant figures. A die is thrown 120 times with the following results. score 2 3 4 5 6 frequency (a) 1 27 12 16 25 26 14 Showing all steps clearly, test whether the die is fair (i) at the 5% level of significance. (ii) at the 1 % level of significance. (7) (b) Explain what is meant by “level of significance” in part (a). (3) (Total 10 marks) 334 501. Give your answers to four significant figures. A sociologist wants to know whether the percentage of sons taking up the profession of their father is the same in every profession. She decides to investigate the situation in each of four professions. She obtained the following data. 63 out of 136 sons of male medical doctors became doctors 42 out of 118 sons of male engineers became engineers 35 out of 96 sons of male lawyers became lawyers 68 out of 150 sons of male businessmen became businessmen At the 5 % level of significance what should her conclusion be? (Total 10 marks) 502. Let ( 4, +) denote the group whose elements are 0, 1, 2, 3, with the operation of addition of integers modulo 4. Let (G, *) denote another group of order four whose elements are a, b, c, d. Let Φ be an isomorphism of ( 4, +) onto (G, *) defined as follows: Φ (0) = b, Φ (1) = d, Φ (2) = a, Φ (3) = c. (a) Write down the group table for ( 4, +). (1) (b) Hence write down the group table for (G, *). (4) (Total 5 marks) 503. Let Y be the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Define the relation R on Y by aRb <=> a2 – b2 ≡ 0 (mod 5), where a, b ∈ Y. (a) Show that R is an equivalence relation. (4) (b) (i) What is meant by “the equivalence class containing a”? (ii) Write down all the equivalence classes. (5) (Total 9 marks) 335 504. Let X be a set containing n elements (where n is a positive integer). Show that the set of all subsets of X contains 2n elements. (Total 6 marks) 505. Let (S, °) be the group of all permutations of four elements a, b, c, d. The permutation that maps a onto c, b onto d, c onto a and d onto b is represented by a b c d c d a b . a b c d . a b c d The identity element is represented by Note that AB denotes the permutation obtained when permutation B is followed by permutation A. (a) a b c d . c a d b Find the inverse of the permutation (1) (b) Find a subgroup of S of order 2. (2) (c) Find a subgroup of S of order 4, showing that it is a subgroup of...
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## This note was uploaded on 06/24/2013 for the course HISTORY exam taught by Professor Apple during the Fall '13 term at Berlin Brothersvalley Shs.

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