MDM4U – FINAL EXAM REVIEW ** For a comprehensive review, you should go through all notes, tests and assignments. Your text also offers review: Cumulative Reviews per Chapter Pg. 218 220 #4, 5, 6, 9, 11, 12, 13, 14, 15, 16 Pg. 364 #1 6, 8 13 Pg. 476 #1 6, 8 Course Review Pg. 477 #1, 4, 5, 7, 8, 9, 10, 11, 14, 15, 17, 19, 21, 22, 23, 24, 26, 27, 28 UNIT: COMBINATIONS AND PERMUTATIONS 1. A survey of 100 Grade 9 students produced the following results. Sport Played Basketball Volleyball Soccer Basketball and Volleyball Volleyball and Soccer Basketball and Soccer All three sports a) Draw a Venn Diagram to represent the situation. b) What is the probability of a student playing only Basketball? c) What is the probability of a student playing only Volleyball or only Soccer? 2. a) b) c) Number of Students 30 30 40 16 14 10 6 Calculate the number of 4 digit numbers you can make with the number 0-9. For all questions all numbers are positive (i.e. there are no negative numbers). Repetition is not allowed. The number is even, repetition is allowed. The 2nd digit is 5 and the number is even, repetition is allowed. 3. Calculate the following: 15 a) 14! b) c) 4 P20,3 d) 10 P2 e) 67! 63! 4. Last week 5 million dollars was stolen from the Gotham City Federal Bank. There was one witness to the crime. The police asked the witness to identify the robber from a line-up of 6 suspects. a) In how many different ways can the 6 suspects be arranged? b) Two of the suspects, The Joker and Batman refuse to stand beside each other. How many different ways can the suspects be arranged? 5. If 5 cards are dealt from a standard deck of 52, answer the following questions: a) How many hands don’t have a face card? b) How many hands have only clubs and diamonds? c) How many hands will have exactly 2 cards of one suit and 3 cards of another suit? 6. a) b) c) A civil jury of 12 members must be selected from 12 males and 13 females. In how many ways can a jury of 12 people be selected from the group? In how many ways can the jury of 4 men and 8 women be selected from the same group? In how many ways can the jury of at least 1 woman be selected from the same group? UNIT: ONE VARIABLE STATISTICS: 1. Below is a table showing the # of employees at a company and their hourly wage. Hourly Earnings ($) 6.00 – 6.50 6.50 – 7.00 7.00 – 7.50 7.50 – 8.00 8.00 – 8.50 8.50 – 9.00 9.00 – 9.50 9.50 – 9.00 # of Employees 3 28 64 56 42 22 2 3 Relative Freqency Cumul. Freq. Midpoint fimi Deviation Deviation fi(mi – x )2 Squared a) Sketch a relative frequency histogram of the data. b) Calculate the mean, median, mode, range and SD of the data. 2. Go through your notes and test/quiz for examples of bias and sampling techniques. 3. A year ago, Mateo began working at a computer store. Her supervisor asked her to keep a record of the number of sales she made each month. The following data set is a list of her sales for the last 12 months: 34, 47, 1, 15, 57, 24, 20, 11, 19, 50, 28, 37 a) Calculate the mean, median, range and SD. b) Determine the quartile values and the interquartile range. Explain the meaning of the interquartile range for this situation. c) Identify any outliers (provide mathematical justification). d) Illustrate the data using a box-and-whisker plot (** Individual data points (within the box-andwisker range) do not need to be drawn). e) What percentiles correspond to sales of 22 and 52 computers? UNIT: TWO – VARIABLE STATS 1. The following data shows the percentage of women in the Canadian work force. year 1950 % women in WF 30 a) b) c) d) 1955 33 1960 30 1965 37 1970 38 1975 39 1980 41 1985 45 1990 47 1995 49 Create a fully labelled scatter plot with a line of best fit. Calculate the correlation coefficient for the data. Determine the equation of the line of best fit. Describe the correlation in terms of type and strength. 2. Go through your notes/test for examples and questions related to cause and effect relationships. 3. Understand the difference between linear and non-linear relationships. Know the difference between a correlation coefficient and a coefficient of determination. UNIT: PROBABILITY AND PASCAL’S TRIANGLE 1. a) b) c) d) e) f) Determine the probability of the following events. Drawing a King from a deck of cards Rolling a number higher than 3 on a six-sided die Drawing a diamond or a heart from a deck of cards Rolling anything but a 2 on an eight-sided die Rolling sum of 2 with 2 six-sided dice Rolling a number greater than 6 rolling with a octahedral (8 sided) die? 2. A bag contains Lego blocks. 3 are red, 5 are blue, and 4 are yellow. 2 Lego blocks are drawn without replacement. a) What is the probability of drawing 2 red blocks? b) What is the probability of drawing a red block, given that the first block was yellow? 3. If Cartman lives at House A and his buddy Kenny lives at House B, how many different routes can Cartman take to Kenny’s house, if he can only walk south and west? 4. a) The probability of an event not occurring is 3 . What are the odds in favour of the event 5 happening? 5 b) The probability of an event occurring is . Determine the odds against the event happening. 9 c) The odds in favour of an event happening is 4:11. What is the probability that the event does not happen? 5. The owner of a fast food restaurant received 25 applications for the position of manager. Of the 25, 15 have worked there before, 8 have a high school diploma, and 5 have both worked there before and have a diploma. What is the probability that a randomly selected applicant has worked there before or has a diploma? 6. There are two tests for aptitude in Data Management (and in particular probability). Test A gives a correct result 95% of the time. Test B is accurate 89% of the time. If a student is given both tests, find the probability that a) Both tests predict the correct result b) Neither test predicts the correct result c) At least one of the predicts the correct result 7. 12 girls and 19 boys (total 31 people) are running for 6 positions on the school’s Graduation Committee. 3 of the 12 girls are sisters, and each candidate is equally likely chosen. Calculate the following: a) b) c) d) What is the probability that all 3 sisters will be on the committee? What is the probability that at least 1 of the sisters will be on the committee? What is the probability that it will be an all boys committee? What is the probability that Meg must be on the committee or it must be an all girls committee? 8. Review examples that used Pascal’s triangle and the patterns in the triangle! UNIT: PROBABILITY DISTRIBUTIONS 1. You must know the 4 types of distributions, when to use them, and examples. 2. Many people believe that high school students are OBSESSED with their cell phones, especially while in Data Management class. If the probability that the teacher will catch a student using their 3 cell phone is . 5 a) Show the probability distribution that the teacher will successfully catch a student using their cell phone 4 days in a row. b) What is the probability the teacher will catch students using their cell phones at least 3 days? 3. There are 6 birds and 8 hamsters in a pet store. Five pets are chosen at random to be relocated to a different store. a) What is the probability that exactly 3 of the pets chosen are birds? b) What is the expected number of birds to be sent to the other store? 4. Homer really wants to stop working at the nuclear power plant. He buys some lottery tickets from the local Kiwiki-Mart. The probability of winning on a ticket is 4 in 20. a) What is the probability Homer will win on his third ticket? b) What is the probability he will win on his first five tickets? c) What is the expected number of tickets Homer would have to buy before winning? 5. Consider a game in which you roll a regular eight-sided die. When you roll an odd number you win an amount of money equal to double the roll. When you roll an even number, you loose an amount of money equal to half the roll. a) What is the expected value of the money received? b) Is this a fair game? Why or why not? UNIT: NORMAL DISTRIBUTION 1. Sketch and provide an example of the following distributions: bimodal, normal, skewed left, skewed right. 2. The lifetime the common house cat ranges uniformly from 10 to 16 years. Determine the probability that a cat selected at random will live less than 11.5 years. 3. 10% of North Americans have blue eyes. There are 850 students at Ancaster High School. What is the probability that exactly 95 of these students have blue eyes? 4. A biologist measures the body length of 100 Japanese sardines. Their lengths are normally distributed, with a mean of 20.20 cm and a standard deviation of 1.65 cm. a) How many sardines have a length less than 22.5 cm? b) What is the probability that a sardine’s length will be between 19.0 and 21.0 cm long?