ADM2303 -Summer 2015 Instructor: Davood Astaraky Assignment two Probability Theory Part I of the assignment : Must be done via MySytatlab Due-date: Monday, June 15, 11:59 P.M. Part II of the assignment : Please don't forget to complete your signed statement of Academic Integrity within the body of your solution Submit a PDF of your type-written (i.e., not handwritten) solution (recall that a submission cannot be marked unless it is in PDF format). Submit your assignment via blackboard learn by due-date Monday, June 15, 11:59 P.M. For this assignment you don't require to use MiniTab, Excel or any statistical tool Make sure to provide detailed calculations and steps of how you arrived at your answer whenever needed. Question 1. Canada conducts a census every ve years. Federal, provincial, and local governments use census data to shape public policy. In 2006, Canada tried something no other country had ever tried - census questionnaires that could be completed online. Sixty-six percent of households completed their census questionnaire by the May 16 deadline. (Households that did not respond by the deadline received follow-up letters and phone calls.) Nineteen percent of households responded online ; sixteen percent of households responded on time and online a) What percent of households led on time or led online ? b) What percent of households did not le on time but used the online service when they eventually responded ? c) What percent of households led on time but did not le online ? d) What percent of households neither led on time nor online ? 1 ADM2303 -Summer 2015 Instructor: Davood Astaraky Question 2. Part one - Seventy-six percent of Ottawans speak English only when they're at home, 10% speak only French, 11% speak a non-ocial language, and the remainder speak more than one language. You are conducting a poll by calling Ottawans at random. In your rst three calls, what is the probability you talk to : a) Only people who speak only English at home ? b) No people who speak only French at home ? c) At least one person who speaks a non-ocial language at home ? Part two - Sixty percent of Ottawans drive their own vehicles to work, 7% ride as passengers in someone else's vehicle, 22% take public transit, 10% walk or cycle, and the remainder get to work some other way. Again you are conducting poll by calling Ottawans at random. In your rst four calls, what is the probability you talk to : a) Only people who drive their own vehicles to work ? b) No one who takes public transit to work ? c) At least one person who walks or cycles to work ? 2 ADM2303 -Summer 2015 Instructor: Davood Astaraky Question 3. A survey of students in a large Statistics for Management class asked about their birth order (1 = oldest or only child ) and which faculty of the university they were studying under. Here are the data : Faculty Art & Sciences Agriculture Human Ecology Other Total Birth order 1 or only 2 or more Total 34 52 15 12 23 41 28 18 57 93 43 30 113 110 223 a) If we select a student at random, what is the probability that the person is an Art & Sciences student who is a second child (or more)? b) Among the Art & Sciences students, what is the probability that a student is a second child (or more) ? c) Among second children (or more), what is the probability that the student is enrolled in Art & Sciences ? d) What is the probability that a rst or only child is enrolled in the Agricultural College ? e) What is the probability that an Agriculture student is a rst or only child ? f) Are enrolling in Agriculture and Human Ecology disjoint ? Explain. g) Are enrolling in Agriculture and Human Ecology independent ? Explain. h) Are being rst-born and enrolling in Human Ecology disjoint ? Explain. i) Are being rst-born and enrolling in Human Ecology independent ? Explain. 3 ADM2303 -Summer 2015 Instructor: Davood Astaraky Question 4. Elizabeth if ying from Moncton to Vancouver with a connection in Montreal. The probability that her rst ight leaves on time is 0.15. If the ight is on time, the probability that her luggage will make the connecting ight in Montreal is 0.95, but if the rst ight is delayed, the probability that the luggage will make it is only 0.65. a) Draw a \"tree diagram\" and organize all the information in the diagram. b) Are the rst ight and leaving on time and the luggage making the connection independent events? Explain. c) What is the probability that Elizabeth's luggage arrives in Vancouver with her ? d) Suppose that her dad picks her up at the Vancouver airport and her luggage is not there. What is the probability that Elizabeth's rst ight was delayed ? 4 BP_Toront BP_Ottawa 134 104 121 114 109 119 126 124 136 105 132 99 126 123 122 102 124 103 125 101 118 120 134 110 115 116 102 110 140 110 118 115 96 113 116 132 122 137 136 101 119 102 111 117 104 106 108 119 119 130 128 121 132 128 141 Wt_Week0Wt_Week4 140 134 136 130 130 126 152 143 134 132 162 153 138 132 148 140 175 165 140 135 137 131 129 125 157 148 144 137 133 130 BP_Toront BP_Ottawa 134 104 121 114 109 119 126 124 136 105 132 99 126 123 122 102 124 103 125 101 118 120 134 110 115 116 102 110 140 110 118 115 96 113 116 132 122 137 136 101 119 102 111 117 104 106 108 119 119 130 128 121 132 128 141 Wt_Week0Wt_Week4 140 134 136 130 130 126 152 143 134 132 162 153 138 132 148 140 175 165 140 135 137 131 129 125 157 148 144 137 133 130