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PENI{ FOSTER COLLEGE INSTRUCTOR USE ONLY GHADE GHADED BY Date: EXAMINATION NO, 050274 Name: Introduction to Business Statistics Proctored Final Examination Instructions: All of the questions on this examination should be answered on the sheets provided, Write your name and your student number at the top of each sheet. Be certain to indicate the proper number before each of your answers. Remember tq show your work if an answer requires a mathematical solution. If you need additional space, you may write on the back of the answer sheets’ Answer any two of the fotlowing four questions, Each answer is worth 2Ao/o. 1. Assume you have a data set from a normally distributed random variable’ Answer the following questions about it. a. Will the random variable be discrete, continuous, or neither? l-{ow’do you know? b. will the data be qualitative or quantitative? How do you know? 2, Assume the following data were gathered by a manufacturer of a robotics component, in unlts of days of continuous use until the component fails. There are 50 measurements in this data set. Show a histogram of this data set with 10 bins of equal size, spanning the range from the data minimum to the data maximum. 14t 139 L29 139 128 L24 139 128 L23 145 L42 135 143 133 t42 150 L47 135 130 136 136 136 127 130 160 133 148 135 161 t47 127 151 136 133 145 118 L27 131 t2L 134 137 154 145 133 131 L22 133 t44 119 125 723 136 1s5 122 120 139 131 L44 t2! 140 (Continued on reverse side) Pr1941,(1204) fi r’oc;{:srarei Finil! Exar.nination 3. A university has been tracking the percentage of alumni giving to its annual fund each year for the past 10 years. The data is given here’ 14o/o 13o/o !5o/o 21o/o L9o/o 24o/o 25o/o 2go/o 25o/o 31o/o Answer the following questions about this data’ a. What are its mean and median? b. What is the procedure for using mean and median to determine whether the data is skewed, and if so, in what direction? c. Apply the procedure you described to the mean and median computed in part a’ 4. A nurse is considering going back to graduate school to earn a Ph’D. in biochemistry’ One of the schools she visits tells her that the average time to earn the degree she’s considering is 5.5 years. Show that this statement is not sufficiently precise by giving two different explanations of what it might mean’ Answer any two of the following three questions. Each answer is wotth t5o/o. 5. In the diagram below, events A, B, and C are shown with numbers in various regions of the graph indicating how many sample points lie in each. For example, the number 3 in the top left of the diagram indicates that there are 3 sample points in B that are not ‘i’;F’i!’ also in either A or C. ‘ .= r :” ‘ a. b” Are the events A Are the events A and B independent? o 8c and C n Bc mutuallY exclusive? Proetored Final Exarnination 6, Under which of the following conditions would it be appropriate to use a Binomial random variable? In each case, explain why your answer is correct’ a. A department will interview 10 candidates for a position, and call back for second interviews those who answer the interview questions to the satisfaction of all the interviewers. They hope to call back at least 3, but past experience suggests an average of about 1 call back per 4 interviews’ b. A factory posts on the wall the number of days since its last safety infraction or injury. In the past year, the factory has had a safety infraction or injury on 6 different days. The factory is interested in the number of days that can be expected to elaPse without an injury. c. Fifteen of a doctor’s patients have the same ailment. Studies have shown that about 86,50lo of patients with this ailment respond to a certain drug. The doctor prescribes the diug to all 15, but the number who will respond in this case is, of course, not known in advance. 7. The mean time for a racecar driver’s crew


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