Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

The number of bacterial colonies of a certain type in samples of polluted water has a Poisson distribution with a mean of 3 per cubic centimeter (cm3). (a) If five 1 cm3 samples are independently selected from this water, find the probability that at least one sample will contain one or more bacterial colonies. (Round your answer to four decimal places.)

Sagot :

Answer:

[tex]P(X\geq 1)= 1 - 0.0497 8 =0.95022[/tex]            

Step-by-step explanation:

Step(i):-

Let 'X' be the random variable in Poisson distribution

Mean of the Poisson distribution λ or ∝ = 3 per  (cm³)

Given n = 5 samples

[tex]P(X=r) = \frac{e^{-\alpha }\alpha ^{r} }{r!}[/tex]

Step(ii):-

The probability that at least one sample will contain one or more bacterial colonies

P(X≥1)    = 1-P(X< 1)

             = 1 - P( X=0)

[tex]P(X\geq 1)= 1 - \frac{e^{-\alpha }\alpha ^{r} }{r!}[/tex]

[tex]P(X\geq 1)= 1 - \frac{e^{-3 }3 ^{0} }{0!}[/tex]

[tex]P(X\geq 1)= 1 - 0.0497 8 =0.95022[/tex]            

                     

                                 

         

Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.