Midterm2-sol - SOLUTIONS Statistics 230, Fall 2010 Midterm...

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Unformatted text preview: SOLUTIONS Statistics 230, Fall 2010 Midterm Test 2 November 18, 2010 Duration: 75 Minutes Family Name: Given Name: ID #: Signature: Section: square 001 - La Croix (12:30-1:20) square 002 - Moshksar (12:30-1:20) square 003 - Struthers (10:30-11:20) square 004 - La Croix (1:30-2:20) square 005 - Moshksar (1:30-2:20) 1. [4 marks] Traffic accidents at the intersection of University Avenue and Westmount Road occur according to a Poisson process with an average rate of 0 . 5 accidents per day. If no accidents occur during a week of seven days, the week is declared a Safe-Week. (a) Find the probability that the week of November 2127 is a Safe-Week. Solution: Accidents occur at the average rate of 0 . 5 accidents per day or (7) (0 . 5) = 3 . 5 accidents per week (7 days). P (Safe-Week) = P (0 accidents in 1 week) = (3 . 5) e 3 . 5 0! = e 3 . 5 . 0302 (b) Find the probability that in a 10 week period there is at most 1 Safe-Week. Solution: Let Y = number of Safe-Weeks in a 10 week period. Then Y BIN (10 , e 3 . 5 ) . P (there is at most 1 Safe-Week in a 10 week period) = P ( Y 1) = P( Y = 0) + P( Y = 1) = parenleftbigg 10 parenrightbigg ( e 3 . 5 ) ( 1 e 3 . 5 ) 10 + parenleftbigg 10 1 parenrightbigg ( e 3 . 5 ) 1 ( 1 e 3 . 5 ) 9 = ( 1 e 3 . 5 ) 10 + 10e 3 . 5 ( 1 e 3 . 5 ) 9 . 9651 . (c) Find the probability that there are 6 accidents during the two week period December 1 14. Solution: Accidents occur at the average rate of 0 . 5 accidents per day or (14) (0 . 5) = 7 acci- dents per two week period (14 days). P (6 accidents in 2 week period) = (7) 6 e 7 6! . 1490 . (d) If 6 accidents occur during the two week period December 114, find the probability that the first week (December 17) was a Safe-Week....
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This note was uploaded on 01/19/2011 for the course STATISTICS 230 taught by Professor Michaella during the Fall '10 term at Waterloo.

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Midterm2-sol - SOLUTIONS Statistics 230, Fall 2010 Midterm...

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