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stats final 2007 - Student Name Student Number Faculty of...

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Student Name: Student Number: Faculty of Science FINAL EXAMINATION Mathematics 203 Principles of Statistics I Thursday, May 31st, 2007 2 p.m. – 5 p.m. Answer directly on the test (use front and back if necessary). Calculators are allowed. One 8.5” x 11” two-sided sheet of notes is allowed. Language dictionaries are allowed. There are 10 pages to this exam and 2 pages of tables. The total number of marks for the exam is 100 Examiner: Dr. Jose Andres Correa Associate Examiner: Professor David Wolfson
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Question 1 (4 points) A survey of residents of a particular community showed that 20% were dissatisfied with the plumbing jobs done. Forty five percent of the complaints dealt with plumber A. If plumber A does 40% of the jobs in the community, what is the probability that a community resident will be dissatisfied with the plumbing job, given that it was done by plumber A? (Show your work). Question 2 (4 points) A die has two sides showing 1 dot each, two sides showing 4 dots each, and two sides showing 9 dots each. Let X be the number that turns up when this die is tossed once. a) Find the probability distribution of X (make a table) (2 points). b) Find the mean and the standard deviation of X (show your work) (2 points). Question 3 (10 points) It is known that 30% of children in Quebec have a genetic predisposition towards a condition which manifests itself as mild obesity in later life. a) What is the probability that in a group of four Quebec children, no more than two of them have this genetic predisposition? (2 points) b) How large would such a group have to be in order that the probability of containing at least one child with the genetic predisposition is at least 0.9? (4 points)
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