×
Get Full Access to Probability And Statistics For Engineers And The Scientists - 9 Edition - Chapter 3 - Problem 86e
Get Full Access to Probability And Statistics For Engineers And The Scientists - 9 Edition - Chapter 3 - Problem 86e

×

# Organisms are present in ballast water discharged from a

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

4 5 1 351 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

Step 3 of 3

## Discover and learn what students are asking

Statistics: Informed Decisions Using Data : The Poisson Probability Distribution
?State the conditions required for a random variable X to follow a Poisson process.

Statistics: Informed Decisions Using Data : Testing the Significance of the Least-Squares Regression Model
?Why is it important to perform graphical as well as analytical analyses when analyzing relations between two quantitative variables?

#### Related chapters

Unlock Textbook Solution