IOE265HW5 - IOE 265 W2007 HW#5 Solutions Due Wed March 7 at...

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IOE 265 W2007 HW #5 Solutions Due: Wed March 7 at 9:00 AM (beginning of lecture) Please include your name, UM ID and lab section time in your written homework assignment. The assignment is worth 20 points (double the usual amount). You may work with other students to discuss problem approaches and check answers, but you may not copy another’s work or refer to solutions from the Instructor’s manual or solutions from previous semesters. Please be sure to staple your assignment if it includes multiple pages. All problems are from the Devore text, 6 th edition. 1. (2.5 points) p. 150, problem #6. a. (0.5 point) b. (0.5 point) k 1 " ( x " 3) 2 [ ] dx 2 4 # = 1 $ k (1 " x 2 + 6 x " 9) dx 2 4 # % & ( ) * = 1 $ k " x 3 3 + 3 x 2 " 8 x [ ] 2 4 = 1 $ k 8 3 " 64 3 + 48 " 12 " 32 + 16 ( ) = 1 $ k = 3 4 c. (0.5 point) Since the prescribed weight is equal to the mean, and this pdf is symmetric about the mean, the probability that the actual weight exceeds the prescribed weight is 0.5.
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d. (0.5 point) First, it is helpful to obtain the cdf of X , which is (for 2<x<4) F ( x ) = k " y 3 3 + 3 y 2 " 8 y [ ] 2 x = " y 3 4 + 9 4 y 2 " 6 y [ ] 2 x = " x 3 4 + 9 4 x 2 " 6 x + 5 . Then the probability that the actual weight is within .25 g of the prescribed weight is F (3.25)- F (2.75) = 0.367. e. (0.5 point) Again using the cdf computed in d), the probability that the actual weight differs from the prescribed weight by more than .5 g is 1-( F (3.5)- F (2.5)) = 1-.688 = .312.
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