MDM4U-Final Exam

MDM4U-Final Exam Name: ______June 2003 Page 1 of 9

Part A – Multiple Choice (1 mark each – 25 total marks)

____ 1. If two variables have no correlation a. the line of best fit has a slope of zero b. a median-median line must be used to predict trends c. the line of best fit has a negative slope d. the points on a scatter plot appear to be random

____ 2. Identify which situation represents two dependent events. a. drawing two cards from a deck without replacement b. flipping a coin twice c. rolling a pair of dice one after the other d. none of the above

____ 3. If X~N , what percent of the data fall between and ? a. 34% c. 50% b. 47.5% d. 95%

____ 4. The expression is equivalent to a. P(14, 6) b. 14C8 c. the number of ways that 6 out of 14 can be arranged d. none of the above

____ 5. For X~N (5, 22) the z-score of x = 4.2 is a. 0.4 c. 0.2 b. 0.2 d. 0.4 MDM4U-Final Exam Name: ______June 2003 Page 2 of 9

____ 6. Drawing from a deck of cards is used to simulate answering a question correctly by guessing on a multiple choice question with four choices. In this simulation, the event of answering a question correctly would be a. drawing a spade c. drawing a heart or diamond b. drawing one of the four aces d. none of the above

____ 7. A bag contains four black marbles and nine orange marbles. If one marble is drawn randomly, determine the odds of pulling out an orange marble. a. 9:4 c. b. 9:13 d.

____ 8. The probability of rolling a number that is divisible by six with a single die is a. c. b. d.

____ 9. In the expansion of , what is the coefficient of the fourth term? a. 10 c. 7 b. 4 d. 5

____ 10. The expression is equivalent to a. 42 c. 21 b. d. none of the above MDM4U-Final Exam Name: ______June 2003 Page 3 of 9

____ 11. Which of the following binomial experiments has the normal approximation with the smallest standard deviation? a. n = 50 and p = 0.45 c. n = 40 and p = 0.55 b. n = 20 and p = 0.45 d. n = 10 and p = 0.55

____ 12. Let set be the set of face cards and be the set of all spades in a regular deck of cards. State which statement is true. a. c. b. d.

____ 13. For the following matrix product, what is the value of x?

a. undefined c. 12 b. 24 d. 42

____ 14. Given that = 0.4, = 0.5, and is 0.6, the value of is a. 1.5 c. 0.3 b. 1 d. 0.1

____ 15. A set of data has the following proporties: mean = 17, median = 15, mode = 14. Which of the following best descibes the data set? a. skewed left c. skewed but neither left nor right b. skewed right d. not skewed

____ 16. A population refers to a. a portion of a group about which data are being collected b. the number of individuals in a group c. the entire group about which data are being collected d. the number of individuals within a given category MDM4U-Final Exam Name: ______June 2003 Page 4 of 9

____ 17. Find the probability that when a single card is drawn from a regular deck of cards a diamond or six is chosen. a. c. b. d. none of the above

____ 18. What is the probability of drawing exactly 2 red cards in a hand of 3 cards drawn from a deck of 52 cards? a. c. b. d.

____ 19. When can the value of a quantitative variable be expressed as a number? a. never c. only if the variable is discrete b. only if the variable is continuous d. always

____ 20. Determine the number of arrangements for the word CANADA. a. 720 c. 240 b. 21 d. 120

____ 21. According to Pascal’s Identity, the single expression of the form , which is

equivalent to ? a. c.

b. d. MDM4U-Final Exam Name: ______June 2003 Page 5 of 9

____ 22. One repetition of an experiment is known as a(n) a. random variable c. expected value b. trial d. occurrence

____ 23. In the expression , which value represents the number of successes? a. 3 c. 5 b. 10 d. 7

____ 24. Find the median and mode (in that order) for the concert ticket prices (in dollars): 35, 55, 38, 35, 37 a. 37, 35 c. 37, 40 b. 28, 35 d. 38, 40

____ 25. Compute the product.

Continue with Part B… MDM4U-Final Exam Name: ______June 2003 Page 6 of 9

Part B – Extended Answer [Marks]

26. A student is writing a multiple choice test consisting of 40 questions, each of which provides four possible choices. He is certain that he has 16 questions correct. If he guesses for all of the remaining 24 questions, what is the probability that he will pass the test? [5]

27. The largest z-score available in most tables is 2.99, which corresponds to a probability of 99.86%. A fair coin is tossed 200 times. What number of heads would be represented by a z-score of 2.99? [4]

28. State the coefficient of the term containing x–11 in the expansion of (4x2 + x–3)7. [6] MDM4U-Final Exam Name: ______June 2003 Page 7 of 9

29. A coin is tossed 20 times in a row. The probability of exactly r heads occurring is given by the term containing pr in the binomial expansion of (p + q)20, where p = q = 0.5. Calculate the probability that exactly 9 heads will be tossed. [3]

30. The eighteenth hole at a public golf course is a par 4. This means that a good golfer should be able to play the hole in 4 strokes. The table below summarizes the scores of a sample of 200 golfers who recently played the hole.

No. of Strokes 1 2 3 4 5 6 7 8 9 10 Frequency 0 3 24 45 51 38 24 9 5 1

What is the expected value for the number of strokes a golfer will take on this hole? [4]

31. A bag contains 12 blocks, 5 of which are red, 4 are blue, and the rest are green. If 7 blocks are selected randomly, determine the number of ways that at least 2 blocks of each color are included. [4] MDM4U-Final Exam Name: ______June 2003 Page 8 of 9

32. A group of vehicles consists of 7 cars and 6 trucks. Five are chosen randomly to be in the show room at a car dealership. Determine the probability that at least one of each vehicle is chosen. [5]

33. The 16 members of the Visual Arts council are seated for a presentation. Determine the probability, in decimal form, that Julie and Tamar will not be seated next to each other. [3]

34. How many of the 250 perch netted by a fisherman would you expect to have a mass more than 400 g, if the distribution of their masses is approximately normal with a mean of 300 g and a standard deviation of 80 g? [4] MDM4U-Final Exam Name: ______June 2003 Page 9 of 9

35. Construct the transition matrix for the following network. [4] A C

36. In a certain Canadian city there are 2 taxi companies: Hillside Cab Co. and Garden Taxi. Market surveys have shown that when people use Hillside there is an 80% chance they will use Hillside the next time. If a person uses Garden, there is only a 60% chance they would choose Garden the next time. a) Construct the transition matrix, P, for this Markov chain. [2] b) If a person called Hillside their first time, what is the probability they will call Hillside the third time a taxi is needed. [4] c) Determine the long term trends by finding the steady state vector. [4]