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GCE JUN 2007 : AS, S1: Statistics1

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ADVANCED SUBSIDIARY (AS) General Certificate of Education 2007 Mathematics assessing Module S1: Statistics 1 AMS11 Assessment Unit S1 [AMS11] THURSDAY 7 JUNE, MORNING 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 log e z AMS1S7 2095 BLANK PAGE AMS1S7 2095 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 (i) Describe, briefly, three distinct features of box plots which make them appropriate for summarising a set of data. [3] There are approximately the same number of boys and girls in the 6th form of a city school. The total times, in hours, that 6th form boys spent watching television during a particular week were recorded. A box plot of the results is shown in Fig. 1 below. 0 5 10 15 20 25 30 Hours Fig. 1 In the same week, the total times that 6th form girls from the same school spent watching television were also recorded. The least time for girls was 2 hours and the longest time was 24 hours. The median time for the girls was 12 hours. The lower and upper quartiles were 9 and 15 hours respectively. (ii) Compare the data sets for the boys and girls. 2 [3] The life expectancy of the talk time of mobile phone batteries may be modelled by a Normal distribution with mean 3.7 hours and standard deviation 0.42 hours. (i) Find the probability that the battery of a randomly selected mobile phone will have a talk time of less than 3.5 hours. [4] (ii) Find the life expectancy exceeded by 25% of mobile phone batteries. [3] (iii) Given that the talk time of a randomly selected mobile phone battery is less than 3.5 hours, find the probability that the talk time is less than 3 hours. [3] AMS1S7 2095 3 [Turn over 3 (a) The manager of a supermarket notes that a checkout assistant always deals with between 8 and 12 customers inclusive in a one hour period on a Friday after lunch. She also notes that the number of customers dealt with follows a discrete uniform distribution. (i) If X is the discrete random variable the number of customers dealt with in this one hour period , construct a table showing the probability distribution of X. [3] (ii) Write down the probability that in this one hour period the checkout assistant deals with at least 10 customers. [1] (iii) Calculate the mean and standard deviation of the discrete uniform distribution. [6] (b) The probability of a customer purchasing vegetables at the supermarket checkout is p. Three customers are chosen at random. The probability that exactly 2 purchase vegetables is the same as the probability that all 3 purchase vegetables. Find the value of p. [4] 4 The number of accidents occurring per day in factories in Northern Ireland for a particular year is recorded. The data is shown in Table 1 below. Table 1 Number of accidents Frequency (days) 0 1 2 3 4 194 122 39 8 2 (i) Show that the mean of this data is 0.636 [2] (ii) Calculate the variance of the number of accidents per day. [2] It is believed that the number of accidents occurring per day follows a Poisson Distribution with mean 0.636 Find the probability that: (iii) exactly 2 accidents occur on a particular day; [2] (iv) 2 or more accidents occur in a 3 day period. [4] AMS1S7 2095 4 [Turn over 5 A shop sells different flavours of ice cream. Of the ice creams sold, 2 are honeycomb flavour. 5 Eight ice creams are sold on a Saturday evening. Calculate the probability that: (i) the first 2 ice creams sold are honeycomb flavour; [1] (ii) at least 2 of the ice creams sold are honeycomb flavour. [4] Suppose that n ice creams are sold at the weekend. Y is defined as the random variable the number of vanilla ice creams sold at the weekend . The probability that an ice cream sold is vanilla flavour is 1 5 The variance of Y is 24 (iii) Find n. (iv) Find E(Y). 6 [3] [2] The continuous random variable X has probability density function f(x) given by k x2 1 0 otherwise x 4 f(x) = 1 (i) Show that k = 21 [4] (ii) Calculate E(X). [3] (iii) Show that the variance of X is 0.527 [5] (iv) Calculate P(2 [3] AMS1S7 2095 X 3). 5 [Turn over 7 A DVD rental company knows that: 20% of its customers rent DVDs on a Monday; 35% of its customers rent DVDs on a Friday; 45% of its customers rent DVDs on a Monday or a Friday. Find the probability that a customer chosen at random from this group of customers: (i) rents DVDs on both days; [3] (ii) rents DVDs only on a Monday. [2] The membership of the DVD rental company is 60% male. A survey carried out by the company found that 70% of males and 55% of females rented DVDs more than 5 times a month. In a particular month, a randomly selected member was found to have rented DVDs 6 times. (iii) Find the probability that the member was female. [5] THIS IS THE END OF THE QUESTION PAPER AMS1S7 2095 6 [Turn over S 2/06 0000 7-009-1 [Turn over

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Additional Info : Gce Mathematics June 2007 Assessment Unit S1 Module S1: Statistics1
Tags : General Certificate of Education, A Level and AS Level, uk, council for the curriculum examinations and assessment, gce exam papers, gce a level and as level exam papers , gce past questions and answer, gce past question papers, ccea gce past papers, gce ccea past papers

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