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Unformatted text preview: 1 ISyE 2028 – Spring 2007 Midterm 1 Solutions Friday 02/09/2007 Time: 09:05  09:55 Calculators are allowed, required statistical tables will be provided. To get partial credit, show all your work. 1. Suppose that only 20% of all drivers come to a complete stop at an intersection having flashing red lights in all directions when no other cars are visible. What is the probability that, of 20 randomly chosen drivers coming to an intersection under these conditions let X be the number of drivers who come to a complete stop. Hence, X ∼ Bin ( n = 20 ,p = 0 . 2). (a) At most 2 will come to a complete stop? P ( X ≤ 2) = 20 2 ! . 2 2 . 8 18 + 20 1 ! . 2 1 . 8 19 + 20 ! . 2 . 8 20 = 0 . 20608 (b) Exactly 5 will come to a complete stop? P ( X = 5) = 20 5 ! . 2 5 . 8 15 = 0 . 17456 (c) How many of the next 20 drivers do you expect to come to a complete stop? E[ X ] = np = 20 * . 2 = 4. 2. A college professor never finishes his lecture before the bell rings to end the period and always finishes his lectures within 1 minute after the bell rings. Let X = the time elapses between the bell and the end of the lecture and suppose the pdf of X is f ( x ) = kx 2 ≤...
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This note was uploaded on 07/30/2008 for the course ISYE 2028 taught by Professor Shim during the Fall '07 term at Georgia Tech.
 Fall '07
 SHIM

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