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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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. 2. (3 points) p. 159, problem #18.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 6

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online