×
Log in to StudySoup

Forgot password? Reset password here

Organisms are present in ballast water discharged from a

Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye ISBN: 9780321629111 32

Solution for problem 86E Chapter 3

Probability and Statistics for Engineers and the Scientists | 9th Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye

Probability and Statistics for Engineers and the Scientists | 9th Edition

4 5 0 247 Reviews
18
2
Problem 86E

Organisms are present in ballast water discharged from a ship according to a Poisson process with a concentration of 10 organisms/m3 [the article ?"Counting at Low Concentrations: • The Statistical Challenges of Verifying Ballast Water Discharge Standards" (Ecological Applications, 2013: 339-351) ?considers using the Poisson process for this purpose]. a. What is the probability that one cubic meter of dis-charge contains at least 8 organisms? b. What is the probability that the number of organisms in 1.5 m3 of discharge exceeds its mean value by more than one standard deviation? c. For what amount of discharge would the probability of containing at least 1 organism be .999?

Step-by-Step Solution:

Answer : Step 1 of 3 : Given, Organisms are present in ballast water discharged from a ship according to a Poisson process with a concentration of 10 organisms/m3 Let X be the organisms in cubic meter. The probability density function of Poisson distribution is e x P(X = x) = x! , where, x = 0, 1, 2, 3, ….. a) The claim is to find the probability that one cubic meter of discharge contains at least 8 organisms Therefore, P( x 8 ) = 1 - P(x 7 ) = 1 - [ P(x = 0) +P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4) + P(x = 5) + P(x = 6) + P(x = 7) ] e10100 e10101 e10102 e10103 e10104 e10105 = 1 - [ 0! + 1! + 2! + 3! + 4! + 5! + e10106 e10107 6! + 7! ] 10 10 x = 1 - [ e x! ] = 1 - [0.0000454(1 + 10 + 50 + 166.67 + 416.667 + 833.33 + 1388.89 + 1987.13] = 1 - 0.2203 P( x 8 ) = 0.7797 Therefore, the probability value is 0.7797. Step 2 of 3 : b) 3 The claim is to find the probability that the number of organisms in 1.5 m of discharge exceeds its mean value by more than one standard deviation the number of organisms in 1.5 m 3 we have 10 organisms/m3 So 10×1.5 = 15 Using the cumulative distribution table for poisson distribution table P(x > + ) = 1 - P(x + ) = 1 - F( 15 + 15) = 1 - F(15 + 3.837) = 1 - F(18.837) = 1 - F(19) = 1 - P(x 19) = 1 - (0.8752) = 0.1248

Step 3 of 3

Chapter 3, Problem 86E is Solved
Textbook: Probability and Statistics for Engineers and the Scientists
Edition: 9
Author: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye
ISBN: 9780321629111

Other solutions

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Organisms are present in ballast water discharged from a

×
Log in to StudySoup
Get Full Access to Statistics - Textbook Survival Guide

Forgot password? Reset password here

Join StudySoup for FREE
Get Full Access to Statistics - Textbook Survival Guide
Join with Email
Already have an account? Login here
Reset your password

I don't want to reset my password

Need an Account? Is not associated with an account
Sign up
We're here to help

Having trouble accessing your account? Let us help you, contact support at +1(510) 944-1054 or support@studysoup.com

Got it, thanks!
Password Reset Request Sent An email has been sent to the email address associated to your account. Follow the link in the email to reset your password. If you're having trouble finding our email please check your spam folder
Got it, thanks!
Already have an Account? Is already in use
Log in
Incorrect Password The password used to log in with this account is incorrect
Try Again

Forgot password? Reset it here