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ADM2303 Final Exam 2005 Fall SemesterQ1 Because cheating has been on the increase the Rector has set up a special investigation As part of this a private investigation company has been engaged and they arrange for one of their agents to register for a particular statistics course The agent finds out that a group of 10 students met at a bar and bought a copy of the midterm quiz and its solution in advance Unfortunately for them the professor who wrote the exam made a rather unusual mistake in the solution to question 2 of the quiz so it is pretty easy to spot who was cheating if their answer matches this mistake There are 65 students registered for the course 4 a4If the marker checks 5 papers as a sample what is the chance none of them belongs to one of the cheaters Be sure to name any methods or models you use and show how you get your answer b In a separate investigation professors belonging to the activist group Cascade Rounding Angers Professors want to correct the improper practice of Cascade Rounding where 123456 is rounded to 124 by first rounding to 12346 then 1235 and finally 124 THIS IS WRONG for those who do it The correct answer is 123 First they want to know how many students do this so set up a calculation where the mean of seventeen numbers is 123456then ask for it to be rounded to the nearest cent The believe fully 12 of students are CR users 4 1b1 2 If they sample 7 papers from a very large collection of exams what is the probability no student cascade rounds Be sure to name any methods or models you use and show how you get your answer3 1b23If they sample 7 papers from a very large collection of exams what is the probability at least 2 students of the seven cascade rounds5 1c5A nationwide study is conducted on cascade rounding and there are many thousands of high school graduates asked to round 123456 to 2 decimals What is the probability that a random sample of 198 such graduates returns less than 12 cascade rounders Bonus Question 2 1d2Suppose you had conducted the study inconly for the U of Ottawa where 546 students were in the population What happens to your answer incSpecify your answer with the new value of the resultingprobabilityQ2 BuzOff is a cosmetics maker that gets its revenue from specialty products that combine cosmetics with insecticides and insect repellents In particular their two key products are a licekilling shampoo Niet and a mosquitorepellent skin cream ZerozDue to the specialty nature of their business Buzoff gets mixed prices for their products However they have fairly good evidence that the average profit per case of Niet is 2345 with standard deviation 129 and for Zeroz is 3123 with standard deviation 245 Because Niet tends to sell better during schooltime when children take too literally their parents advice to share at least where lice are concerned while Zeroz gets sold mainly in the summertime when mosquitos are active the correlation between profits of these two products is 04muN 2345 sigmaN129 muZ 3123 sigmaZ 2454 2a4If Buzoff sells 1225 cases of Niet and 3543 cases of Zeros what is the coefficient of variation ofthe resulting profit
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