6:22 4 Part A (Putting the Concepts to Work): Completion ( 6 marks): Using your reading, answer the following questions: For each question you are asked to: a) identify the information given in the question. b) determine the appropriate formula. c) substitute the values given into the formula and find the solution. d) give the final answer. e) as part of your answer, give the page number in the reference material or the website that you used to find the answer to the question. 1. If there are two possible outcomes in a distribution, then the distribution must be (two marks) A uniform C hypergeometric B binomial any of the above 2. On a game show, the winning prize is behind door #1, door #2, or door #3. If the location of the winning prize is selected at random, the distribution of the number of times in one week it is behind door #3 is(two marks) uniform C hypergeometric binomial D none of the above MDM4U Lesson Assignment Page 1 3. The names of six adults and ten children in a family are written on pieces of paper and put in a hat. Five different slips of paper are drawn from a hat. Identify whether the number of children's names drawn is a binomial or hypergeometric distribution and how to convert it to the other type. (two marks) A Hypergeometric; draw the names with replacement. Binomial; draw the names with replacement. Hypergeometric; draw the names without replacement. D Binomial; draw the names without replacement. Part B (Terminology): Matching ( 34 marks ) Using your readings, match each term with the correct definition provided. The name of the term is given in the table and the definitions are listed below. Match the name of the term and the corresponding definition. As part of your answer, identify the sources of your information. Each question is worth 2 marks. - one for the matching and one mark for your proof. Match the correct type of probability distribution to each of the following characteristics. A probability distribution may be used more than once or not at all. A uniform distribution B binomial distribution C hypergeometric distribution D uniform or binomial distribution E binomial or hypergeometric distribution 1. all outcomes are equally likely 2. trials are dependent 3. trials are independent 4. successful outcomes are counted 5. E(X) = np ahwdsb.elearningontario.ca6:22 4 6. P(x) = _ 7. E(x) = La Match the correct expectation formula to each of the following probability distributions. A formula may be used more than once or not at all. A * D np 2x, P(x, ) i-1 B ap E ra C 8. uniform distribution 9. binomial distribution 10. hypergeometric distribution 11. all discrete probability distributions Match the correct term to each of the following descriptions. A term may be used more than once or not at all. A expectation probability distribution B discrete random variable probability histogram C uniform distribution G random variable D continuous random variable 12. This type of variable has an infinite number of values. 13. This type of variable has only certain values within a given range. MDM4U Lesson Assignment Page 3 14. Shows the entire list of outcomes in an experiment and their probabilities. 15. This is also known as the predicted average of a set of outcomes. 16. Shows the relative frequencies of a set of outcomes. 17. A quantity that can have a range of values that are due to chance. Part C (Putting the Concepts to Work): Completion (28 marks): Using your reading, answer the following questions: For each question you are asked to: a) identify the information given in the question. b) determine the appropriate formula. c) substitute the values given into the formula and find the solution. d) give the final answer. e) as part of your answer, give the page number in the reference material or the website that you used to find the answer Ohwdsb.elearningontario.ca6:23 4 Part C (Putting the Concepts to Work): Completion (28 marks): Using your reading, answer the following questions: are asked to: 5 of 7 on given in the question. riate formula. riven into the formula and find the solution. e) as part of your answer, give the page number in the reference material or the website that you used to find the answer to the question. 1. A club has 21 members, four of whom are executives. Five members are randomly selected to take part in a survey. a) What is the probability that four non-executive members are chosen? b) What is the expected number of non-executive members? (four marks) MDM4U Lesson Assignment Page 4 2. State which type of distribution (uniform, binomial, hypergeometric, none of these) would model each situation. (six marks) a) Drawing eight names out of a hat without replacement and recording the number of females. b) Generating random numbers between 1 and 100 and recording the number of prime numbers in 20 trials. ) Selecting the winning ticket in a raffle. d) Noting the wait time before you reach the front of a line. e) Recording the number of doubles when rolling two standard dice. f) Recording when the first occurrence of a red jelly bean occurs while selecting jelly beans from a bag. 3. A card is repeatedly cut from a standard deck, with replacement, for a total of five cuts. The number of aces is recorded.(four marks) a) Is this a binomial or hypergeometric distribution? Why? b) Rewrite the situation to convert it to a hypergeometric or binomial distribution, as appropriate. ahwdsb.elearningontario.ca