JZ Second_Exam

JZ Second_Exam - Problem 1 2 3 4 5 6 7 8 Earned 12 12 12 9...

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Problem Value Earned 1 12 12 2 12 12 3 12 12 4 12 9 5 13 13 6 13 13 7 13 9 8 13 13 Total 100 93 Problem 1) The following (fictitious) data was collected based on a random sample of SUV accident Auto Manufacturer Broad Tire Company Fjord Engines Kreuger Total Waterrock 158 202 90 450 Misterlin 70 90 40 200 Greatmonth 122 158 70 350 Total 350 450 200 1000 a) Given that an SUV accident has occurred, what is the probability that it was a Fjord SUV P(Fjord ) = 0.35 b) Given that the SUV in the accident had Waterrock Tires, what is the probability that it wa P(Fjord | Waterrock Tires) = 0.35 c) Given that an SUV accident has occurred, what is the probability that the SUV had Wate P(SUV accident | Waterrock Tires) = 0.45 d) Given that the SUV involved in the accident was a Fjord, what is the probability that it ha P(Waterrock Tires | Fjord) = 0.45
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e) Based on your answers above what do you think about the relationship between Waterr From the results we got we can say that Waterrock is not independent of Fjord as P(Fjord | Waterrocks Tires) not equal to P(Fjor
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ts: V? as a Fjord SUV? errock Tires? ad Waterrock Tires?
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rock tires and Fjord SUV's? rd). They are almost equal but not exactly the same.
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Problem 2) A food processor claims that at most 10 percent of his jars of instant coffee conta less coffee than claimed on the label. To test this claim, 20 jars of his instant coffee a randomly selected and the contents are weighed. Using statistical techniques, he fin that if 4 or fewer of the twenty jars contain less coffee than claimed on the label, his manufacturing process is in control. a) Find the probability that 4 or fewer of the twenty jars contain less coffee than claimed on the label, if the manufacturing process is actually producing only five per that are underweight. P(jars <= 4) = 1 b) Find the same probability if the process actually produces 10 percent underweigh P(jars <= 4) = 0.96 c) Find the same probability if the process actually produces 15 percent underweigh P(jars <= 4) = 0.83
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in are nds rcent t. t.
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Problem 3) At a checkout counter customers arrive at an average rate of 2.1 per minute. Find the probabilities that a) at most four customers will arrive in any given minute; P(Customers <= 4) = 0.94 b) at least three customers arrive during an interval of two minutes; mean = 4.2 P(customers <= 2) = 0.21 P(Customers >= 3) = 1- P(Customers <= 2) = 0.79 c) at most 15 customers will arrive during an interval of six minues; mean = 12.6 P(Customers <= 15) = 0.8
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Problem 4) In order to satisfy customers that the amount of instant coffee in a four ounce jar actually contains at least four ounces of coffee, a manufacturer sets his filling process to have a mean of 4.10 ounces with a standard deviation of .05 ounces. If the process follows a normal distribution,
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JZ Second_Exam - Problem 1 2 3 4 5 6 7 8 Earned 12 12 12 9...

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