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# ADM2303 ASSIGNMENT FOUR - PART TWO SAMPLING DISTRIBUTIONS

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Author: Christine Farr
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ADM2303 -Summer 2015Instructor: Davood AstarakyAssignment Four - Part twoSampling DistributionsPart I of the assignment :• Must be done via MySytatlab• Due-date: Monday, July 27, 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 bemarked unless it is in PDF format).• Submit your assignment via blackboard learn by due-date Monday, July 27, 11:59 P.M.• Make sure to provide detailed calculations and steps of how you arrived at your answer whenever needed.Question 1.When a truckload of apples arrives at a packing plant, a random sample of 150 is selected and examined forbruises, discoloration, and other defects. The whole truckload will be rejected if more than 5% of the sampleis unsatisfactory. Suppose that 8% of the apples on the truck do not meet the desired standard. What is theprobability that the shipment will be accepted anyway ?Question 2.The average January temperature in Calgary varies from year to year. These average January temperaturesthemselves have an average, over many past years, of -7.9 degrees Celsius, with a standard deviation of 5.0degrees. Assume a Normal model applies.a) During what percentage of years does Calgary have a January average above 0 degrees ?b) In the 20% coldest Januaries, the average January temperature reaches no higher than how many degrees ?c) Suppose you will be in Calgary for the next four years. Describe the sampling distribution model for theaverage of the next four January average temperatures. Assume climatic conditions are not changing.d) What is the probability that the average of the next four January average temperatures will exceed -4 degrees? If this happens, would you consider this evidence of climactic warming (at least locally in Calgary), orjust Normal variations ?

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