The number of bacteria colonies of a certain type in

Chapter 3, Problem 197SE

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QUESTION:

Problem 197SE

The number of bacteria colonies of a certain type in samples of polluted water has a Poisson distribution with a mean of 2 per cubic centimeter (cm3).

a If four 1-cm3 samples are independently selected from this water, find the probability that at least one sample will contain one or more bacteria colonies.

b Howmany1-cm3 samples should be selected in order to have a probabilityof approximately .95 of seeing at least one bacteria colony?

Questions & Answers

QUESTION:

Problem 197SE

The number of bacteria colonies of a certain type in samples of polluted water has a Poisson distribution with a mean of 2 per cubic centimeter (cm3).

a If four 1-cm3 samples are independently selected from this water, find the probability that at least one sample will contain one or more bacteria colonies.

b Howmany1-cm3 samples should be selected in order to have a probabilityof approximately .95 of seeing at least one bacteria colony?

ANSWER:

Solution 197SE

Step1 of 3:

Let us consider a random variable Y it presents the polluted water by certain type of bacteria colonies. Here Y follows poisson distribution with parameter

Here our goal is:

a). We need to find the probability that at least one sample will contain one or more bacteria colonies. When four 1cm3 samples are independently selected from this water.

b). We need to check how many 1cm3 samples should be selected in order to have a probability of approximately 0.95 of seeing at least one bacterial colony.


Step2 of 3:

a).

Here 4 1cm3 samples are independently selected from this water then the value of is given by:

     

The probability mass function of poisson distribution is given by:

y = 0,1,2,...,n

The probability that at least one sample will contain one or more bacteria colonies is given by:

                 

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