2008 solutions

# 2008 solutions - MATH 203 Final Examination Student Name...

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Unformatted text preview: MATH 203 Final Examination April 21, 2008 Student Name: Student Number: McGill University Faculty of Science FINAL EXAMINATION MATH 203 Principles of Statistics I April 21st, 2008 9 a.m. - 12 Noon Answer directly on the test (use front and back if necessary). Calculators are allowed. One 8.5” × 11” two-sided sheet of notes is allowed. Language dictionaries are allowed. There are 15 pages to this exam and 2 pages of tables. The total number of marks for the exam is 100. Examiner: Professor Russell Steele Associate Examiner: Professor David Stephens 1 MATH 203 Final Examination April 21, 2008 Question 1: (10 points) Presbyterian Hospital in Pittsburgh, Pennsylvania keeps records of emergency room traffic. Those records show that the times between arriving patients have a mean of 8.7 minutes with a standard deviation of 8.7 minutes. (a) Based solely on the values of the mean and standard deviation, explain why it is unrea- sonable to assume that the times between arriving patients is normally distributed (or even approximately so). [5 points] Answer: The mean of the arrival times is 8.7 minutes with a standard deviation of 8.7 minutes. Using the Empirical Rule, a mound-shaped and symmetric distribution would have approximately 95% of the observations symmetrically distributed from 8 . 7 − 2 ∗ 8 . 7 to 8 . 7 + 2 ∗ 8 . 7, or (-8.7, 26.1). However, we obviously can’t have negative waiting times, so that means the empirical rule CANNOT hold, so it would be unreasonable to assume that the times between patients would be normally distributed. CONTINUED ON NEXT PAGE 2 Here is a histogram of a random sample of size 10,000 of inter-arrival times: 10,000 hospital between arrival times times Between arrival times Frequency 20 40 60 80 100 1000 2000 3000 4000 (b) Sketch a picture of what the general shape of a Q-Q normal plot should be for this sample of data (assuming that the sample quantiles are for the standardized wait times) on the blank plot below. [5 points] Normal Q-Q Plot Theoretical Quantiles Sample Quantiles-4-2 2 4-4-2 2 4 3 MATH 203 Final Examination April 21, 2008 Question 2: (8 points) Professor Steele and his younger brother play on-line Go Fish (a particular card game) every day, but because they’re so busy, they can only play two games per day. The winner of each game wins \$5 from the other person and we can assume, because of his statistical prowess, Professor Steele wins 40% of the games against his brother. Also you can assume that the two games that they play every day are independent (and the games between days are also independent). (a) Consider the random variable that is the number of dollars that Professor Steele wins from his brother tomorrow from their on-line game of Go Fish. Define what type of random variable this is (discrete or continuous) and then appropriately define the probability mass function or probability density function for that random variable. [4 points] Answer: This is a discrete random variable because he can only win \$10 (wins both...
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2008 solutions - MATH 203 Final Examination Student Name...

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