Exam 2 - Solutions

# Exam 2 - Solutions - STATISTICS 321 Dr Soma Roy Exam 2(4...

This preview shows pages 1–2. Sign up to view the full content.

STATISTICS 321 – Dr. Soma Roy Name : Exam 2 – May 21, 2009 (4 sides ) Maximum points: 50 1. Consider writing onto a computer disk and sending it through a certifier that counts the number of missing pulses. Suppose this number X has a Poisson distribution with parameter λ = 0 . 2. (a) (2 points) Show that the probability that a randomly selected disk has exactly one missing pulse is equal to 0.16. Let X = number of missing pulses on a disk, X Poisson ( λ = 0 . 2). Then, we want P ( X = 2) = e - 0 . 2 0 . 2 1 1! = 0 . 16 (b) (4 points) What is the probability that 3 disks that are independently selected will have fewer than 2 missing pulses in total ? Let Y = 3 X = total number of missing pulses on 3 disks, Y Poisson ( λ = 3 × 0 . 2 = 0 . 6). Then, we want P ( Y < 2) = P ( Y = 0) + P ( Y = 1) = e - 0 . 6 0 . 6 0 0! + e - 0 . 6 0 . 6 1 1! = 0 . 88 (c) (4 points) If 5 disks are independently selected, what is the probability that 2 of the disks each contain exactly one missing pulse? Let W = number of disks, each with one missing pulse in a sample of 5 disks, W Binomial (5 , . 016) (From (a)). Then, we want P ( W = 2) = 0 . 15 2. (8 points) A machine that produces ball bearings has initially been set so that the true average diameter of the bearings it produces is 0.500 inches. A bearing is acceptable if its diameter is within

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

View Full Document
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