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Mathematics - Higher Module 1 - Statistics November 2004 Section A ( Calculator)

Mathematics - Higher Module 1 - Statistics November 2004 Section A ( Calculator). Question 1 relative frequency Question 1X raffle tickets calculate profit Question 2 cumulative frequency graph Question 3 stratified sample Question 4 random numbers and probability.

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Mathematics - Higher Module 1 - Statistics November 2004 Section A ( Calculator)

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  1. Mathematics - Higher Module 1 - Statistics November 2004 Section A ( Calculator) Question 1 relative frequency Question 1X raffle tickets calculate profit Question 2 cumulative frequency graph Question 3 stratified sample Question 4 random numbers and probability

  2. 1. Kali has a spinner with coloured sections of equal size. She wants to know the probability that her spinner lands on pink. She spins it 100 times and calculates the relative frequency of pink after every 10 spins. a) Use the graph to calculate the number of times the spinner landed on pink after 10 spins and after 50 spins 0.6 X 10 = 6 0.44 X 50 = 22 4 Marks From the graph estimate the probability of the spinner landing on pink 1 Mark Answer = 0.4

  3. c) Kali’s results confirm that her spinner is fair. The spinner has 5 sections. How many sections are pink? 1 Mark 0.4 = 4/10 = 2/5 ( 2 sections out of 5) Answer = 2 Kali spins the spinner two more times. What is the theoretical probability that the spinner lands on pink both times? 0.4 X 0.4 = 0.16 2 Marks

  4. 1X. A charity sells raffle tickets for 50p. The winning prize is £100. 50 people bought 1 ticket each 80 people bought 2 tickets each 70 people bought 3 tickets each 95 people bought 4 tickets each 40 people bought 5 tickets each Calculate how much profit the charity made on this raffle Number of tickets sold: (50 X 1) + (80 X 2) + (70 X 3) + (95X 4) + ( 40 X 5) 50 + 160 + 210 + 380 + 200 = 1000 Take in 1000 X 50p = £500 4 marks Make 500 -100 = £400 profit

  5. 2. The journey times of 80 commuters are shown on the cumulative frequency diagram below. Use the diagram to estimate a) The median journey time 1 Mark Answer = 54 Estimate the interquartile range UQ = 74 LQ = 40 IQR =34 2 Marks

  6. 3) A College wants to obtain a sample of its student population. The college decides to take a stratified sample of size 200 by ethnic group. The table shows the student population by ethnic group. Total 1450 Show that the college should choose 26 Asian students as part of its sample 186/1450 X 200 = 25.6 ( 26 to the nearest whole number) 2 Marks Calculate the number of students the college should choose for each ethnic group White: 725/1450 X 200 = 100 Black: 388/1450 X 200 = 54 Other: 151/1450 X 200 = 21 All rounded to nearest whole number 3 Marks

  7. 4. A computer is used to generate three – digit random numbers from 000 to 999. e.g. 006, 000, 977, 125……….. Given that a generated number is a multiple of 3, find the probability that it is also a multiple of 4. 000, 003, 006,……….999 are all multiples of 3 There are 333 (or 334) possibilities of a number being a multiple of 3 If a number is a multiple of 3 and a multiple of 4 then it is a multiple of 12 1000 / 12 = 83.3333 There are 83 (or 84) possibilities Given that it is a multiple of 3 then probability that it is a multiple of 4 is 84/334 (0.251) or 83/333 (0.249) 4 marks

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