ductory Statistics Third Edition Perdisco Assessment Below is a set of assessable homework questions on this topic, selected by your professor. Take care! Do not submit your answers until you have read all the instructions and answered the questions carefully. When you submit your answers, you will receive immediate feedback. Navigating this page: Submit answers: Submit your answers for immediate grading Bookmark: Save this question set so that you can come back to it later 1 of 2 ID: MST.FET.P.ANOP.01.0040A [2 marks] marks] Two friends, Helen and Harriet, have a coin. Helen spent all day flipping the coin thousands of times, and observed that it turned up heads 60% of the time. So Helen assigns a probability of 0.6 to the event that a head turns up. Harriet, who is unaware of Helen's flipping experiment, reasons that the coin has two sides, each side being equally likely to show up. So Harriet assigns a probability of 0.5 to the event that a head shows up. a) The process that demonstrated relative frequency probability was: reasoning that the outcomes of the coin flip are all equally likely flipping the coin many times and observing the outcomes both reasoning that all outcomes are equally likely and observing the coin flips made b) A weakness with the probability assigned by Helen is that: it must be wrong, the probability must be 1/6 it is an estimate probability has nothing to do with how often an event is seen to occur 2 of 2 ID: MST.FET.P.ANOP.02.0010A [1 mark] mark] Four students attempt to describe the likelihood of an event. They all assign a probability to this event. The table to the right shows each student together with the probability that they have assigned. Based only on this information, the student that believes that the event is impossible is: Karen Natalie Linda Miranda Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Sunday, April 17, 2016, 08:47 http://www.perdisco.com.au Student Probability Karen 0 Linda 0.5 Miranda 1 Natalie 2 Introductory Statistics Third Edition Perdisco Assessment Below is a set of assessable homework questions on this topic, selected by your professor. Take care! Do not submit your answers until you have read all the instructions and answered the questions carefully. When you submit your answers, you will receive immediate feedback. Navigating this page: Submit answers: Submit your answers for immediate grading Bookmark: Save this question set so that you can come back to it later 1 of 2 ID: MST.FET.P.ANOP.01.0030A [2 marks] marks] Two friends, Helen and Harriet, have a coin. Helen spent all day flipping the coin thousands of times, and observed that it turned up heads 60% of the time. So Helen assigns a probability of 0.6 to the event that a head turns up. Harriet, who is unaware of Helen's flipping experiment, reasons that the coin has two sides, each side being equally likely to show up. So Harriet assigns a probability of 0.5 to the event that a head shows up. a) A relative frequency approach to probability is demonstrated by: Helen Harriet both Helen and Harriet b) A weakness with the probability assigned by Helen is that: it must be wrong, the probability must be 1/6 it is an estimate probability has nothing to do with how often an event is seen to occur 2 of 2 ID: MST.FET.P.ANOP.02.0030A [1 mark] mark] Four students attempt to describe the likelihood of an event. They all assign a probability to this event. The table to the right shows each student together with the probability that they have assigned. Student Probability Karen 0 Based only on this information, the student that believes that the event is certain is: Linda 0.5 Miranda 1 Natalie 2 Natalie Miranda Linda Karen Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Friday, April 15, 2016, 16:04 http://www.perdisco.com.au Introductory Statistics Third Edition Perdisco Assessment Below is a set of assessable homework questions on this topic, selected by your professor. Take care! Do not submit your answers until you have read all the instructions and answered the questions carefully. When you submit your answers, you will receive immediate feedback. Navigating this page: Submit answers: Submit your answers for immediate grading Bookmark: Save this question set so that you can come back to it later 1 of 3 ID: MST.FET.P.FP.01.0020A Consider the random process of rolling a 12-sided die. The sample space is the set of numbers 1 to 12 and you can assume that the die is fair (i.e. each outcome is equally likely). The events A and B are defined by: Event A: you roll a number greater than 4. Event B: you roll a number less than 5. a) Regarding the events A and B, select the correct statement: A and B are mutually exclusive A and B are not mutually exclusive there is not enough information to tell whether or not A and B are mutually exclusive [2 marks] marks] 12-sided die A 12-sided die is just what is sounds like! It is a die with 12 sides. The sides are all the same size and shape so the die is a regular 12-sided polygon called a dodecahedron. (In fact it is a platonic solid.) This is important if every number is going to have a equal chance of being rolled. b) Regarding the events A and B, select the correct statement: A and B are collectively exhaustive A and B are not collectively exhaustive there is not enough information to tell whether or not A and B are collectively exhaustive 2 of 3 ID: MST.FET.P.FP.02.0030A [3 marks] marks] Little Inc. is having a board meeting to decide which medium to use in a new advertizing campaign. Little Inc. doesn't have many resources to dedicate to advertizing and so they can only use one of the following methods: television radio internet newspaper billboards Margot thinks that an airwave broadcast campaign would be most effective and so she hopes that the board will either decide to use television or radio. Noah believes that they should focus on visual advertizing and thinks billboards or television would be best. Let A be the event that the board decides on either television or radio. Let B be the event that the board decides on either billboards or television. a) The event that the board decides on television is the . b) The event that the board decides on either internet or newspaper or billboards is the . c) The event that the board decides on either television, radio or billboards is the 3 of 3 ID: MST.FET.P.FP.03.0020A . [1 mark] mark] A survey of 1,000 apartment dwellers asks the question: 'How many bedrooms are in your apartment?'. For a randomly chosen respondent, let A denote the event that the respondent's apartment has 2 or more bedrooms, and B denote the event that the respondent's apartment has 2 or less bedrooms. Events A and B are Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Friday, April 15, 2016, 16:05 http://www.perdisco.com.au but not . Introductory Statistics Third Edition Perdisco Assessment Below is a set of assessable homework questions on this topic, selected by your professor. Take care! Do not submit your answers until you have read all the instructions and answered the questions carefully. When you submit your answers, you will receive immediate feedback. Navigating this page: Submit answers: Submit your answers for immediate grading Bookmark: Save this question set so that you can come back to it later 1 of 3 ID: MST.FET.P.CAP.01.0040A [2 marks] marks] A group of 1000 people are surveyed and asked two questions; whether they own a computer and whether they use a computer at their workplace. The results are presented here: 526 154 149 171 people people people people own a computer and use a computer at work own a computer but do not use a computer at work do not own a computer but use a computer at work do not own a computer and do not use a computer at work Define the events A and B to be: A: a randomly chosen person owns a computer B: a randomly chosen person uses a computer at work A student who is studying this situation went about calculating the probability that a person owns a computer or uses one at their work. The student did this by counting up all of the people that own a computer, and then counting up all of the people that use a computer at their work. They then added these two numbers together and divided by 1000 to find P(A or B). a) A Venn diagram showing events A and B is given: Four regions in the diagram are marked V1, V2, V3, V4. In using the method that they did, select the region that is over-counted by the student: V1 V2 V3 V4 b) Calculate the correct probability that a random person owns a computer or uses a computer at their work. Give your answer as a decimal to 2 decimal places. P(owns a computer or uses a computer at work) = 2 of 3 ID: MST.FET.P.CAP.02.0020A [3 marks] marks] Craig owns a simple steakhouse restaurant, Pull Up Steaks, and he is thinking of making some changes: he wants to broaden the menu and he wants to put a bar in the restaurant. One weekend he hands out the following questionnaire to the diners: FEEDBACK How were we? Here at Pull Up Steaks our number one priority is your dining satisfaction and we are always trying to find new ways of achieving this. So we have a couple of questions ... Do you think we should expand our menu? YES / NO Do you think we should include a bar in our restaurant? YES / NO Craig gets 264 responses. The results of this survey are displayed in the following contingency table: Menu Expansion Restaurant Bar Yes No Yes 34 28 No 135 67 Complete these statements using the information in the above table. Give your answers to parts a) and b) to the nearest whole number. Give your answer to part c) as a decimal to 2 decimal places. a) The number of respondents that do not want the restaurant bar is . b) The number of respondents that want at least one of the changes that Craig has proposed is . c) The probability that a respondent chosen at random will want at least one of the changes that Craig has proposed is . 3 of 3 ID: MST.FET.P.CAP.03.0020A [3 marks] marks] A student at a university has been doing a project to investigate entertainment habits of students. They have surveyed 100 random students who were each asked three questions: 1. Have you watched a movie in the last week? 2. Have you listened to music in the last week? 3. Have you read a book in the last week? However, the student keeps a very messy room and has lost some of the results. They have been able to find the following results: Of all the students surveyed, 42 had watched a movie, 40 had listened to music and 42 had read a book in the last week. Also: 7 students answered yes to all three questions 10 students answered yes to questions 1 and 2 only 10 students answered yes to questions 1 and 3 only 15 students answered yes only to question 1 21 students answered no to all three questions Find the missing information and answer the following questions regarding the group surveyed. Give your answers as whole numbers. Calculate the number of students that: a) answered yes to question 2 only = b) answered yes to exactly one question = c) had watched a movie or read a book but had not listened to music = Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Friday, April 15, 2016, 16:05 http://www.perdisco.com.au Introductory Statistics Third Edition Perdisco Assessment Below is a set of assessable homework questions on this topic, selected by your professor. Take care! Do not submit your answers until you have read all the instructions and answered the questions carefully. When you submit your answers, you will receive immediate feedback. Navigating this page: Submit answers: Submit your answers for immediate grading Bookmark: Save this question set so that you can come back to it later 1 of 3 ID: MST.FET.P.CP.01.0030A [7 marks] marks] Your friend has been busy studying the statistics of their favorite football team and wants your help. They are interested in looking at how the team fairs during wet matches, i.e. games played in wet weather, compared to dry matches. They have researched the team's playing history and found that the team has played a total of 500 games of which 281 were dry matches and 222 were wins. Further, the team has had 60 wins in wet matches and 162 wins in dry matches; and also the team had 159 losses in wet matches and 119 losses in dry matches. Let the events A and B be: Event A: a random game is a wet match Event B: a random game results in a win a) An incomplete tree diagram for this scenario is presented. Fill in the appropriate probability for each part of the tree. Give your answers as decimals to 2 decimal places. Win Dry match Loss Win Wet match Loss b) Find the probability that a random game results in a win given that it is a wet match. Give your answer as a decimal to 2 decimal places. P(B given A) = 2 of 3 ID: MST.FET.P.CP.02.0040A [6 marks] marks] A survey of 1,000 people is conducted to study how support for a new government initiative differs between people from rural and urban backgrounds. The 1,000 people are made up of 500 people from urban areas and 500 people from rural areas. Each person is asked whether or not they support the government proposal. The results of the survey show that 163 are rural and support the proposal; 337 are rural and do not support the proposal; 183 are urban and support the proposal; and 317 are urban and do not support the proposal. a) A tree diagram describing this situation has been drawn up, and some probabilities have been filled in. Complete the tree diagram for this scenario by filling in the appropriate probability for each part of the tree. Give your answers as decimals to 2 decimal places. Does support Rural 0.5 Doesn't support Does support Urban 0.5 Doesn't support Let the events A and B be: Event A: a random person from the survey is from a rural area Event B: a random person from the survey doesn't support the proposal b) Find the probability of A and B Give your answer as a decimal to 2 decimal places. P(A and B) = c) Find the probability of B given A. Give your answer as a decimal to 2 decimal places. P(B|A) = 3 of 3 ID: MST.FET.P.CP.03.0030A [2 marks] marks] For the random process of rolling two six-sided dice and recording the sum, let A and B be the events defined by: A: the result is an even number B: the result is less than or equal to 8 a) Calculate the probability of B given A. Give your answer as a decimal to 2 decimal places. P(B|A) = b) Calculate the probability of A given B. Give your answer as a decimal to 2 decimal places. P(A|B) = Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Friday, April 15, 2016, 16:05 http://www.perdisco.com.au Answers a. both Helen and Harriet b. it is an estimate c. Linda 1 of 3 ID: MST.FET.P.FP.01.0020A a. A and B are mutually exclusive b. A and B are collectively exhaustive 2 of 3 ID: MST.FET.P.FP.02.0030A The event that the board decides on television is 1/5. The event that the board decides on either internet or newspaper or billboards is the 1/5 +1/5 = 2/10 The event that the board decides on either television, radio or billboards is the 1-(1/5+1/5+1/5) = 2/5 3 of 3 ID: MST.FET.P.FP.03.0020A Events A and B mutually exclusive are but not independent. 1 of 3 ID: MST.FET.P.CAP.01.0040A a. V2 b. 526 people own a computer and use a computer at work 154 people own a computer but do not use a computer at work =(526+154)/1000 =680/1000 2 of 3 ID: MST.FET.P.CAP.02.0020A a. =28+67= 95 b. =34+135= 169 c. =169/264 3 of 3 ID: MST.FET.P.CAP.03.0020A 7 students answered yes to all three questions 10 students answered yes to questions 1 and 2 only 10 students answered yes to questions 1 and 3 only 15 students answered yes only to question 1 21 students answered no to all three questions a. =(15+10)/42 =25/42 b. 15/42 c. =(10+15)/42 1 of 3 ID: MST.FET.P.CP.01.0030A a. b. c. d. e. f. Dry Matches = 281/500 Wet match = 222/500 Win Dry matches = 162/281 Win Wet matches = 60/222 Lose dry matches = 159/281 Lose wet matches = 119/222 Find the probability that a random game results in a win given that it is a wet match. Give your answer as a decimal to 2 decimal places. P(B given A) P(B). P(A and B) = P(A)P(B) P(6, 0, 0) + P(0, 6, 0) + P(0, 0, 6) + P(6, 6, 0) + P(6, 0, 6) + P(0, 6, 6) + P(6, 6, 6) = 3x(1/6 x 5/6 x 5/6) + 3x(1/6 x 1/6 x 5/6) + (1/6 x 1/6 x 1/6) = 75/216 + 15/216 + 1/216 = 91/216 2 of 3 ID: MST.FET.P.CP.02.0040A a. b. c. d. Rural - Do notr support 0.5 Urban Do not support 0.5 Rural Support 0.5 Urban Support 0.5 b. Find the probability of A and B Give your answer as a decimal to 2 decimal places. P(A and B) = 0.5 c. Find the probability of B given A. Give your answer as a decimal to 2 decimal places. P(B|A)= 1/2 x 1/2 x *1/2 3 of 3 ID: MST.FET.P.CP.03.0030A a. Calculate the probability of B given A. Give your answer as a decimal to 2 decimal places. P(B|A) = 1/2 x 1/2 x *1/2 b. Calculate the probability of A given B. Give your answer as a decimal to 2 decimal places. P(A|B) = 15/16