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GCE MAY 2008 : AS, S1: Statistics1

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ADVANCED SUBSIDIARY (AS) General Certificate of Education 2008 Mathematics assessing Module S1: Statistics 1 AMS11 Assessment Unit S1 [AMS11] THURSDAY 29 MAY, AFTERNOON TIME 1 hour 30 minutes. INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number on the Answer Booklet provided. Answer all seven questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. You are permitted to use a graphic or scientific calculator in this paper. INFORMATION FOR CANDIDATES The total mark for this paper is 75 Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question. A copy of the Mathematical Formulae and Tables booklet is provided. Throughout the paper the logarithmic notation used is ln z where it is noted that ln z loge z AMS1S8 3191 BLANK PAGE AMS1S8 3191 2 [Turn over Answer all seven questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 The histogram in Fig. 1 below shows the number of hours worked in one week by the one hundred employees of an electronics company. Six employees worked less than five hours. Histogram showing hours worked by employees in one week 3 2.4 2 1.8 Frequency density 1.6 1.2 1 0 05 15 20 35 45 50 Hours Fig. 1 Calculate estimates for the mean and standard deviation of the number of hours worked by the employees of this electronics company. [7] AMS1S8 3191 3 [Turn over 2 In a particular city in 2007, it was known that 18% of children younger than two years had anaemia. On a particular day in 2007, a doctor examined 11 children under two years old in the city. By using the Binomial distribution, find the probability that: (i) exactly 2 will have anaemia; (ii) more than 2 will have anaemia. 3 [3] [5] During a certain period on a Monday morning, an average of 4 customers enter a shopping centre per minute. It is known that the number of customers entering the shopping centre during this period may be modelled using a Poisson distribution. (i) State two necessary conditions when modelling using a Poisson distribution. [2] Find the probability that: (ii) no customers enter during a particular minute; (iii) 3 or more customers enter during a particular minute; [4] (iv) exactly 3 customers enter during a thirty second period. 4 [2] [3] Packets of cereal are filled in such a way that the masses of their contents are Normally distributed with mean 520 g and standard deviation 15 g. The labels on the packets state that the mass of cereal contained is 500 g. Find the percentage of packets: (i) which will contain less than 500g of cereal; [4] (ii) which will contain more than 525g of cereal. [4] The mean mass of the cereal can be altered without affecting the standard deviation. (iii) Find the new mean value which will ensure that only 2% of the packets contain less than the labelled mass. [3] AMS1S8 3191 4 [Turn over 5 The probability density function f(x) of a continuous random variable X is given by k (5 x x 2 4) f (x) = 0 1x4 otherwise where k is a constant. (i) Find the value of k [6] The graph of y = f(x) is shown in Fig. 2 below. y 1 4 x Fig. 2 5 (ii) Explain why the mean of this distribution is 2 [1] (iii) Find the variance of the distribution. [7] AMS1S8 3191 5 [Turn over 6 In a game of chance, a bag contains two gold and four black counters. A player selects a counter at random from the bag without replacement. When a gold counter is drawn, the game ends. Otherwise, the player draws again until a gold counter is picked. Let X be the discrete random variable the number of selections required until a gold counter is drawn . (i) Copy and complete Table 1 below. Table 1 Number of draws x 1 2 3 4 5 P(X = x) [5] (ii) Find E(X) (iii) Find Var(X) 7 [2] [4] An internet auction company is conducting a survey about the ages of married couples who use its services. 4 For any married couple, the probability that the husband is over 25 is and that his wife 5 1 is over 25 is 2 The probability that the husband is over 25 given that his wife is over 25 is 19 0 A married couple is chosen at random. 9 (i) Show that the probability that both husband and wife are over 25 is 20 [2] Using a Venn diagram or otherwise, find the probability that (ii) only one of the couple is over 25 [4] (iii) neither one of the couple is over 25 [2] Two married couples are chosen at random. (iv) Find the probability that only one of the husbands is over 25 and only one of the wives is over 25 AMS1S8 3191 6 [5] [Turn over S 11/06 530-067-1 [Turn over

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Additional Info : Gce Mathematics May 2008 Assessment Unit S1 Module S1: Statistics1
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