UNCP MAT 2100 - EXAM 2 (2 pages)

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EXAM 2



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EXAM 2

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Pages:
2
School:
University of North Carolina at Pembroke
Course:
Mat 2100 - Intro to Statistics
Intro to Statistics Documents

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MAT 210 Spring 2006 Name Exam 2 Class Code 03 31 2006 Write your full name and code clearly on the first page of your solutions This is an open book notes test Work independently Please do not write on the test One page per question only 50 minutes Total score is 100 Good luck Part I Probability Conditional Probability Bayes Theorem 50 pts 1 25 pts 5 pts each You are going to toss a coin repeatedly in successive trials until you get a head for the first time and then you are going to stop the experiment Assuming that the coin is unbalanced with P head 1 5 answer the following questions 1 Draw a tree diagram that is used to determine the outcomes 2 List at least 4 possible outcomes 3 Express the event at least 4 tosses are required in terms of the outcomes 4 Compute the probabilities P at least 4 tosses are required before the experiment terminates 5 Explain why the probability calculated in 4 is large Geometric Distribution In problems 3 and 4 below the number of Bernoulli trials n is fixed while the number of defective items or international requests is the variable One has dependent trials selections without replacement and the other has independent trials selections with replacement or without replacement but only few items are selected from a large number of products In the first probability model given in problem 1 trails are independent and the number of trials required until certain event occurs is the variable This model is the so called Geometric distribution 2 25 pts 25 3 pts each Bayes Theorem A test for a certain disease is found to be 95 accurate meaning that it will correctly diagnose the disease in 95 out of 100 people who have the ailment The test is also 95 accurate for a negative result meaning that it will correctly exclude the disease in 95 out of 100 people who do not have the ailment For a certain segment of the population the incidence of the disease is 4 1 If a person tests positive find the probability that the person actually has the



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