Canadian International Matriculation Programme Sunway University College MDM 4U MATH OF DATA MANAGEMENT FINAL EXAMINATION Date: November, 2008 Time: 8.30a.m 10.30a.m Length: 2 HOURS Lecturers: (Please circle your teacher s name) Ms. Chia Yeng, Pn. Dzura, Mr. Nithya, Dr. Gandhari, Mr. Welch Student Name: Section/Period: Please read the following instructions carefully before you begin the examination: 1. This exam paper has fourteen printed pages, including this cover page. 2. The examination is worth 30 percent of your final mark. 3. The examination consists of three parts: PARTS A, B and C. PARTS CONTENT MARKS TIME ALLOCATION A Multiple Choice 15 20 MINS B Short Answer 25 40 MINS C Problem 60 60 MINS TOTAL 100 4. The answers to the Multiple Choice Questions must be written on page 12 of this booklet. All other answers must be written in the space provided. If you need more space, continue on the blank page to the left of the relevant question and do indicate your intention. 5. Scientific or graphing calculators are permitted, but NO sharing is allowed. 6. You can ONLY use the special function of the graphing calculator when you see the symbol below. Otherwise, use the common functions only. GC 7. Marks for each question are indicated inside square brackets, [ ]. 8. Normal Distribution table and Formula sheet are at the rear of this booklet - Pages 13 & 14. For office use only: Part A Part B Part C Total Page 1
PART A Multiple Choice [15 marks] Identify the letter of the choice that best completes the statement or answers the question. DO REMEMBER TO PLACE YOUR ANSWERS ON PAGE 12 OF THIS BOOKLET 1. Which of the following would exhibit a negative correlation? I Number of days a person spends at a slimming centre and his/her weight. II The speed of a car and the time taken to reach its destination. III The age of a used car and its resale price. IV Length of a person s hair and her height. a. I, II and IV c. I, II and III b. I and II only d. All of the above 2. In the expression, which value represents the number of trials? a. 2 c. 5 b. 3 d. 8 3. Determine the number of different arrangements for the word BOBBIE. a. 240 c. 720 b. 120 d. 6 4. A histogram has a bin width of 0.5. The left end point of the first interval is 7.25. What is the left end point of the sixth interval? a. 9.75 c. 12.25 b. 10.25 d. 13.25 5. Which statement regarding the probability distribution for a binomial experiment with p = 0.5 is not true? a. The probability of no successes must equal the probability of no failures. b. The graph of the distribution is symmetrical. c. The expected value of the experiment is half the number of trials. d. The more trials that are made, the higher the probability that all trials will be successful. 6. The mean of a set of 5 numbers is 26. What would the mean be if one of the numbers was increased by 10? a. 10 c. 28 b. 26 d. 36 7. In a stem-and-leaf plot, the leaves represent the a. frequency of a data category b. final digits of the values in a data category c. initial digits of a data category d. average of the data values 8. A table displays 3 red blocks, 2 green blocks, and 4 blue blocks. Calculate the number of different ways the blocks can be arranged in a row. a. 1260 c. 362 880 b. 15 120 d. none of the above Page 2
9. Two variables have a coefficient of determination of 0.81. The correlation coefficient could be a. 0.81 c. 0.9 b. 0.43 d. 0.66 10. Students were asked whether they would prefer a cat or a dog for a pet. The results are shown in the following graph. Which of the following conclusions is valid? a. females are more likely to prefer cats over dogs b. most students prefer cats c. males and females are equally likely to prefer dogs d. there is no correlation between gender and pet preference 11. Identify which situation represents two dependent events. a. drawing two cards from a deck and the first is put back b. taking out two marbles from a bag one after another c. rolling two dice one after another and recording the result of each d. none of the above 12. The men that shop for clothes at the Hard-to-Fit Shoppe are typically unusually short or unusually tall. The distribution of their heights is likely to be a. U-shaped c. mound-shaped b. uniform d. skewed 13. Which of the following is not a property of a normal distribution? a. the median and mode are equal b. the area under a normal curve is 1 c. it is symmetric about the mean d. 99.7% of the data is within 2 standard deviation of the mean 14. Use the standard deviation to determine which of the two baseball teams has been more consistent in its scoring for the last five games. Ontario: 0, 4, 2, 3, 6 Alberta: 3, 3, 3, 5, 7 a. Ontario c. they are equally consistent b. Alberta d. it cannot be determined 15. If X~N(12.4, ) and 95% of the data lie in the interval 11.8 13.0 the σ equals a. 1.2 c. 0.09 b. 0.3 d. 0.06 Page 3
PART B Short Answer [25 marks] Show your working in the space provided. 16. The stem-and-leaf plot below shows the daily number of visitors to a museum. Stem Leaf 5 5 9 6 1 3 9 9 9 7 0 8 2 6 9 6 8 10 1 4 4 4 8 11 3 3 8 i) Determine the median of the above data set. ii) Identify the shape that best describes this distribution. 17. A group of 3 students is randomly taken from a class of 15 students. Determine the probability that Mary and Susan will always be in this group. [3 marks] 18. The masses in grams of seven kittens in a litter are: 400, 450, 500, 500, 550, 650, 800. How many of the kittens have a mass within one standard deviation of the mean? Hint: Use the graphing calculator (GC) to compute the standard deviation. [3 marks] Page 4
19. An internet site has an average of 2500 hits per day. The number of daily hits is normally distributed with a standard deviation of 220. For how many of the next 50 days would you expect the site to receive fewer than 2280 hits? [3 marks] GC 20. An experiment was conducted to determine stopping distance of a vehicle at various speeds. The following results were observed and recorded: Speed (km/hr) Stopping Distance (m) 35 50 65 70 75 80 95 105 16 25 41 43 50 62 88 110 i) Perform a quadratic regression analysis and write the equation correct to 4 decimal places. ii) State the coefficient of determination and briefly explain its meaning. 21. The following graph represents the popularity of different foods among a group of high school students. Unfortunately, the vertical scale is missing. If 18 students preferred hamburgers, how many students preferred tacos? Page 5
22. Note: The entries within each part of the circle represent the quantity of the elements and are not the elements themselves. (Example: n(a) = 5 + 1 + 2 + 3 = 11) Compute the following probabilities based upon the diagram above. i) P( B C D) [1 mark] ii) P ( A B ) 23. The management of Supermarket A has prepared the following charts to compare the pricing of their fresh produce to those sold at Competitor X. Supermarket A Competitor X 4.50 4.00 3.50 3.00 2.50 2.00 1.50 1.00 Banana Watermelon Papaya Tomato Cabbage 4.50 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00 Banana Watermelon Papaya Tomato Cabbage i) What is the impression conveyed by these graphs? [1 mark] ii) Suggest a way to improve the graph for the information to be represented more accurately. Page 6
PART C Problem [60 marks] Show your complete working in the space provided. 24. The following broken-line graph displays the depth of snow over a 2-day period. i) What was the maximum depth of snow? [1 mark] ii) Estimate the mean snow depth during the first 6 hours. Show your calculation steps below. iii) What information does the graph provide between 20 and 26 hours? 25. Answer the following questions based upon your understanding of the properties of normal distribution and the usage of the z-score table: i) A person s IQ is normally distributed with a mean of 100. Which are there more of: people with an IQ less than 80 or people with an IQ greater than 110? Explain. ii) Freya was using a z-score table and noticed that. She saw that this pattern holds for other z-scores. Explain why this pattern occurs. Page 7
26. A bag contains 4 chocolate bars, 3 pretzels and 5 doughnuts. Two items are taken out from the bag one after another and without being replaced. i) Would you classify the events of taking out the items one after another to be independent or dependent? Explain briefly. ii) Calculate the probability that the first item is a pretzel and the second would be a doughnut. iii) Calculate the probability that either the first item removed is a chocolate bar or the second item removed is a doughnut. Hint: Solve the problem with the use of the appropriate probability formula. [5 marks] 27. A student writes a three question multiple-choice quiz. Each question has four possible responses. The student guesses at random for each question. Create a probability distribution to show all possible scores on the quiz. [6 marks] X = Page 8
28. A survey of 120 swimmers from Sunway University College was conducted of which 90 were found to frequent the college swimming pool where else 30 prefer to swim outside the college. Among those who use the college swimming pool, it was determined that 20% would prefer to swim during the weekend (i.e.: Saturday or Sunday). Among the students who prefer to swim outside, it is known that 60% prefer swimming on a regular day (i.e.: Monday to Friday). a) Construct a tree diagram to illustrate the outcomes and probability breakdown of the above problem. [4 marks] b) Use the tree diagram to calculate the following: i) the probability that a person selected at random would swim at the college pool on a regular day (i.e.: Monday to Friday); ii) the probability that a person would not use the college pool although we know that he/she prefers swimming during the weekend (i.e.: Saturday or Sunday) 29. The weight (in g) of 10 packs of sweets are as follows : 30, 22, 30, 50, 53, 47, 49, 35, 28, 45 Draw a box-and-whisker-plot and include all necessary measures to show the spread of the distribution, and their respective values. [5 marks] Page 9
30. The owner of a small retail business wants to determine the relation between weekly advertising expenses and weekly sales. His records show the following : GC Advertising Expenses (RM) Sales (RM) 40 480 20 400 25 395 20 425 30 475 50 500 45 490 20 420 50 555 40 525 i) With the aid of graphing calculator, sketch the scatter plot for the above data set using the scale shown below. Sales 600 ($) 300 10 60 Advertising Expenses (RM) ii) Compute the equation of the regression line (4 decimal places) for the above data set. [1 mark] iii) Find the correlation coefficient (3 decimal places) and describe the type of correlation. iv) Based upon the regression line, how much should the owner budget for his advertising expenses if he wants to achieve weekly sales of RM600? v) An advertising agency wants to convince the owner that a small increase in advertising expenses can yield a much bigger increase in sales. Briefly describe the changes he can make to the display of the graph in part i) in order to create this impression. Page 10
31. The masses of 500 boxes of sugar are approximately normally distributed with a mean of 150g and a standard deviation of 2.5g. i) What percent of the boxes will have a mass greater than 155g? [3 marks] ii) How many of these boxes would you expect to have a mass less than 145g? [3 marks] 32. A teacher of a class of 45 students is trying to decide whether her class will play hockey, soccer or basketball. She surveys the class and finds out that 21 students like hockey, 28 like soccer, 25 like basketball, 16 like hockey and soccer, 10 like soccer and basketball, and 11 like hockey and basketball and 2 do not like any of the three sports. i) Draw a Venn diagram to illustrate the above information. Use x to denote the number of students who like all three sports. [4 marks] ii) Determine the number of people who like all three sports. iii) Find the probability that a student chosen at random would like only two of the sports. (Note: Remember to complete the multiple choice answer sheet on the next page) ***** END OF PAPER **** Page 11
MULTIPLE CHOICE ANSWER SHEET NAME : PERIOD : Answer all multiple choice questions on this sheet 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. Page 12
FORMULA SHEET Chapter 3 Normal Dist. x x z= or s z = x µ σ n( A) P ( A) = n( S) P( A) = 1 P( A') P ( A = P( A) + P( or P( A = P( A) + P( P( A Chapter 4 Probability P( A P( A = P( P ( A = P( A) P( or P ( A = P( A P( P ( n, r) n! = ( n r)! n = r ( n n! r )! r! n! = n ( n 1) ( n 2)... 3 2 1 Chapter 5 Probability Distribution P n x = Ε( X ) xp( x) x x X x p q n ( = ) = ( np x Ε X ) = Page 13