IOE265HW5

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

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

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.

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

View Full Document
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.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern