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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.)

Answer :

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]            

                     

                                 

         

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